Karnataka 2nd PUC English Textbook Answers Springs Chapter 8 To the Foot from its Child

To the Foot from its Child Questions and Answers, Notes, Summary

To the Foot from its Child Comprehension I

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Question 1.
What would the foot like to be?
OR
Mention one of the things that the child’s foot likes to be.
The foot would like to be a butterfly or an apple.

Question 2.
‘The child’s foot is not yet aware it’s a foot’ (line 1 of the poem) conveys
a. the immense possibilities of life
b. the unrestricted nature of a child’s imagination
c. the child’s ignorance of harsh realities.
(b) and (c) the unrestricted nature of a child’s imagination/the child’s ignorance of harsh realities.

Question 3.
What does time teach the child?
Time teaches the foot that it cannot fly and also cannot be a fruit on the branch of a tree.

Question 4.
The line ‘stones and bits of glass, streets, ladders and the paths in the rough earth’
a. indicates hardships one has to face in life.
b. provides a mere description of a road.
c. suggests the good and bad experiences of growing up.
(a) indicates hardships one has to face in life.

Question 5.
Why does the child’s foot feel defeated?
The child’s foot feels defeated because it has to live like a prisoner, condemned to live in a shoe, and it can never be free to escape from the difficulties of life.

Question 6.
Mention the words that convey the real experiences of the foot.
The words ‘stones and bits of glass, streets, ladders, and the paths in the rough earth’ convey the real experiences of the child’s foot.

Question 7.
Identify the lines in the poem that suggest the transformation of the foot.
Lines 17 – 28 suggest the transformation of the foot.
“These soft nails
of quartz ………
…………………….
……………………
a coarsening hard to accept.”

Question 8.
“….. condemned to live in a shoe” suggests that the foot is
(a) a prisoner
(b) a criminal
(c) forced to give up its dreams.
(a) and (c) a criminal/forced to give up its dreams.

Question 9.
What does the line ‘until the whole man chooses to stop’ mean?
OR
When does the foot stop to walk in Neruda’s poem?
The line, ‘until the whole man chooses to stop’ means until the person dies.
OR
The foot stops to walk when the person dies.

To the Foot from its Child Comprehension II

Question 1.
We think of a foot as a part of the human body, but Neruda says ‘To the Foot From its Child’. Why?
We think of a foot physically as belonging to a person but Neruda sees in a philosophical way and says “To The Foot From Its Child”. Though it belongs to a person physically, philosophically like the child who is the symbol of innocence, the foot also does know about its future. But in adulthood, it faces many challenges of life and gets an overall experience and leads a meaningful life until the end. Finally, it is attacked by diseases and surrendered to death.

Question 2.
Pick out the expressions that suggest the child’s imagination is fertile.
The expressions, ‘to be a butterfly’, or ‘an apple’, ‘can not fly’, ‘cannot be a fruit bulging on the branch’ suggest that the child’s imagination is fertile.

Question 3.
What contrasting descriptions of the foot does the poem offer? Why?
The poet Pablo Neruda presents a contrasting description of a child’s foot and an adult’s foot so as to delineate the changes that are seen in a person’s life as he or she changes from an infant into an adult, until his death. Initially, the child or the infant’s foot has soft nails of quartz and its toes are tiny, soft, and rounded at the tips like the petals of some flowers.

As the child learns to walk and starts walking on stones, bits of glass, streets, ladders and the rough surface of the earth, the child’s foot becomes aware of its role. It learns that it is a foot and cannot become a butterfly or a bulging fruit on a tree. Once it realizes that it is a foot, it is defeated in realizing its aspirations and gets imprisoned in a shoe. Inside the shoe, it tries to understand the world in its own way, alone, like a blind man groping in the dark. During this period its soft nails of quartz become opaque, are bunched together, and look like eyeless reptiles with triangular heads, grow callused, and are covered with faint volcanoes of death.

These changes happen because, once the child’s foot becomes an adult’s foot, it walks as the foot of a man or woman and keeps walking in the fields as a farmer, or as a grocer in the markets, or as a miner in the mines or as a church minister or a government worker, until its death. Thus, the foot experiences the hardships of life and loses its ‘soft’ and flowery petal-like form.

Question 4.
The poem begins with the idea that a child’s foot is not yet aware that it is afoot; at the end, the foot is unaware that it had ceased to be afoot. What is the poet trying to convey through these statements?
OR
Explain the similarity between the foot’s early life and its end as depicted in ‘To the Foot From its Child’.
In this poem, ‘foot’ is a metaphor for ‘life’. The poet Neruda using the foot as a metaphor to explore ‘life’ through its various stages from infancy through childhood until death.

When the poem begins, the ‘foot’ is the infant’s foot which suggests man’s ‘childhood’. The child’s foot does not know that it is a foot. This state refers to the innocence of childhood where ‘Man’ has many dreams and aspirations. The child’s wish to become a butterfly or an apple stands for man’s aspirations and dreams. Once the child’s foot enters the real world, it starts walking over stones, bits of glass, streets, ladders, and the rough surface of the earth.

Thus, as the child grows over a period of time, the child’s foot realizes that it is only a ‘foot’ and cannot become fruit or a butterfly. Then, since it has to serve its role as afoot, it is imprisoned in a shoe. Inside the shoe, it tries to understand the world alone, in isolation. The child’s foot, as it grows old, serves as the foot of a man or a woman working in the fields, or market or mines or ministries and toils hard day and night until it dies. When it dies, the foot loses its human awareness and that is why when it is buried the foot again gets its child-like innocence. It again dreams of becoming an apple or a butterfly. It is this journey from childhood through adulthood and the final death that the poem focuses on.

Pablo Neruda is saying that life and death are part of a continuous cycle. Secondly, the poet wishes to say that the freedom of childhood is lost when a person becomes an adult and faces a life of constant work and struggle. Thus, life takes away people’s free spirits until they are freed again by death.

Question 5.
How does Neruda describe the busy life of the individual as represented by the foot?
The ‘foot’ is used as a metaphor for life and the foot refers to the foot of an individual. Once the child develops into an adult, the adult keeps on walking without respite either as a man or as a woman. The individual spends his life working either as a farmer in a field, or as a miner in mines, or as a salesperson in the market or as a government servant or as a church minister. This way the individual toils hard in society until his death.

Question 6.
What does the last stanza of the poem mean? Can you think of parallels in nature?
In this poem, ‘foot’ is used as a metaphor for ‘life’. Life refers to the life of a human being as seen from his infancy until his death. Pablo Neruda gives his view of ‘life’ and ‘death’ in this poem. The poem does not begin with the beginning of life in the womb of its mother but from the time after it has taken birth on the earth. The poem covers the period of its infancy to death and beyond. The ‘foot’ as portrayed in the poem refers to the child’s foot. Since a child is not aware of its limitations and lives in a dream world of imagination, the child’s foot wishes to fly like a butterfly or become a bulging apple on the branch of a tree. Over a period of time, it realizes that it is only a foot and its role is only to serve as a foot.

The poet then refers to the ‘adult food’ after death or an individual after death. Once a human being dies, he or she is normally buried. It is this burial of the dead body of the individual that is expressed in the line “it descended underground unaware, for there, everything was dark”. Once the ‘foot’ or the individual dies, it loses its human awareness and goes back to its child-like innocence. This is expressed in the sentence ‘It never knew it had ceased to be a foot’. That is why, like a child’s foot which is not aware that it is only a ‘foot’, it aspires to become a butterfly and fly or become an apple.

One can find several parallels in nature. All living beings born on the earth pass through the cycle of birth and death. A seed germinates to give a seedling. The seedling grows into an adult plant, may become a tree or a shrub, and die. Its seeds bring a similar plant to life again. Similarly, the eggs of animals hatch and bring forth their young ones which grow, mature, lay eggs and later die. Their eggs bring back similar animals to life again.

To the Foot from its Child Comprehension III

Question 1.
Examine how Neruda’s poem works out the contrast between colourful dreams and the humdrum reality of life.
OR
The poem ‘To the Foot From its Child’ represents the conflict between illusion and reality. Elaborate.
The poem, ‘To the Foot from its Child’, presents a contrast between colourful dreams and the humdrum reality of life. The poet conveys his view of life through his description of a foot. The foot is a metaphor for expressing the crushing of a child’s spirit through the challenges and restrictions that life places upon him. One can undoubtedly infer that the poem is basically a criticism of how people force children to grow in society and forget all their dreams and imaginations.

With a view to delineating the forces that capture the child’s freedom and aspirations, the poet begins the poem making a statement directly that the child’s foot, which is not aware that it is a foot, would like to be a butterfly or an apple. From this one can infer that man’s spirit dreams of enjoying unlimited freedom in this world but it comes to know that it cannot enjoy unlimited freedom and has to pass through several obstacles before it matures into an adult.

But, in time, stones and bits of glass, streets, ladders, paths in the rough earth go on teaching the foot that it cannot fly. As the infant is growing and developing into a mature adult, he is exposed to the harsh realities of life which are metaphorically expressed as stones, bits of glass, ladder, street, etc. These are the problems and obstacles an individual has to face. Thus, once the child becomes a boy, an adolescent, and an adult, the problems of life teach the individual that he is a ‘mortal’ and his powers are limited and can only serve the society as a member like other human beings. This sense is expressed in the line ‘that it cannot fly, cannot become a fruit and is defeated, falls in the battle, is a prisoner condemned to live in a shoe’. Here, the ‘shoe’ can be taken to mean the human society that regulates his mind and activities.

Wearing the shoe refers to the infant becoming a mature adult. Soon after entering adulthood, the individual explores ‘life’ within the shoe. He loses touch with the reality of the outside world but experiences the world through the eyes of society. This again means that a lot of restrictions are imposed on the individual. Now that he is an adult he keeps on walking without respite through the fields, mines, markets, and ministries. The line ‘this foot toils in its shoe, scarcely taking time to bare itself in love or sleep’ expresses the fact that once he realizes that he is a man destined to live in a society, he learns to face the humdrum realities of life. He has no time to let his human spirit indulge in ‘love’ and ‘sleep’. He is a prisoner and keeps on working until he dies. Once he dies his spirit loses its human awareness and is once again as free as the children.

Question 2.
Neruda’s poem is a salute to the ordinary human being, who continues with life braving all odds. Do you agree? Give reasons.
Yes. In this poem, Neruda tries to delineate the journey of human ‘life’ from its infancy to death and beyond. With a view to expressing the changes that the ‘life spirit’ undergoes through its journey from an infant to an adult and beyond death, Neruda uses ‘foot’ as a metaphor. That is why he calls ‘life’ during infancy as the infant foot and the life spirit of an adult as the adult foot.

The whole poem can be summed up as the ‘surrender’ of life force to societal pressures. During infancy, the child’s spirit dreams of infinite possibilities and hence dreams of becoming a fruit or a butterfly. Once it starts growing in society the harsh realities of life expressed as ‘stones, bits of glass, ladder, and rough surface of the earth’, teach the infant spirit that it is a ‘foot’ which means ‘you have a role’ to play in the society and ‘you are an individual subservient to the whims and fancies of the society’. Once the infant spirit gradually accepts its defeat and tries to live in conformity with the norms of the society, it becomes an adult. This is expressed metaphorically as the ‘foot being imprisoned in a shoe’.

In the poem, Neruda does not speak of the possibilities of the human spirit ‘rebelling’. Nor does he say that human spirit is being crushed by oppressive forces; the human spirit does not commit suicide. On the contrary, he describes the journey of the human spirit as an infant’s foot until it becomes an adult foot and after its death how it becomes free again. From this, it can be argued that Neruda’s poem is a salute to the human spirit for braving all odds and completing one’s cycle of life and death peacefully, and not rebelliously.

Question 3.
Is Neruda criticizing how society crushes childhood dreams and forces people into rigid moulds?
OR
“Society crushes dreams of individuals and condemns them to live in captivity.” Explain with reference to ‘To the Foot from its Child’.
Yes, to some extent. In this narrative-descriptive poem, Neruda has attempted to delineate the predicament of man as a prisoner enslaved by society. Using ‘foot’ as a metaphor for ‘life’, he narrates the journey of life from that of an ‘infant foot’ to an ‘adult foot’ until its death and after. In the first two lines itself, the poet declares the wish of childhood. The infant’s foot is not aware that it is a ‘foot’ and hence would like to be a butterfly or an apple. These two objects – ‘butterfly’ and ‘apple’ – together suggest that the infant’s foot thinks of complete freedom to become whatever it wants. Being born a human being it cannot aspire to become a butterfly or an apple.

From this, we can infer that there is some restriction imposed on us by birth itself. This is expressed in the line ‘it is not aware that it is afoot’. The infant food, once it starts growing, is exposed to the ways and means of the world. We live in human society and nature, the words ‘stones, bits of glass, streets, ladders, and the paths in the rough earth’ refer to man’s ways of living. This exposure to man’s style of living brings awareness in the child that it is a foot. The poet suggests that the infant’s foot is engaged in a battle with the society and ‘adults’ crush the child’s playful spirit and imprison it in a shoe. This stage refers to the way the child gets acclimatized to living in human society.

Once it wears the ‘shoe’, which means, it accepts its identity as ‘man’, a member of the human society, he starts exploring the human world alone, groping in the dark like a blind man. There is a difference in the way an adult explores the world. As a child, it thinks of infinite possibilities; but, as an adult, it is aware of its limitations. This means the society has been successful in crushing childhood dreams and forcing the life spirit into the rigid moulds of society.

Since the whole poem only describes various changes undergone by the human spirit, we cannot say that Neruda is criticizing society for its stranglehold on the human spirit. Secondly, Neruda also says that the child’s foot does not know that it is a foot. This means, even Neruda knows that the child is born a human being and is going to live in human society. Thirdly, nowhere in the poem does Neruda say anything against societal forces. However, Neruda sympathises with ‘Man’ at one point. He says, ‘this foot toils in its shoe scarcely taking time to bare itself in love or sleep’. These lines indicate that Neruda only sympathises with man’s predicament and does not criticize society.

Question 4.
‘Foot’ is a keyword in the poem. Comment on Neruda’s skillful use of the word and its associations in terms of imagery to convey his ideas.
OR
Highlight the imagery used to bring out life’s hardships that deform the child’s foot.
In this poem, as the title ‘To the Foot from its Child’ suggests, ‘foot’ is the keyword in the poem. The poet uses ‘foot’ as a metaphor for his view of ‘life’. The poet personifies the ‘foot’ and focuses his attention on the ‘life’ of man, using the ‘foot’ as the protagonist. ‘Life’ begins in infancy and so even in the poem, ‘life’ begins as an infant’s foot.

It is natural that children, who are naive and innocent, do not know that their foot is meant for walking and it has a function to discharge. Through the use of the ‘foot’ as a metaphor, the poet cleverly brings out the battle between harsh realities of life symbolically expressed as stones, streets, ladder, bits of glass, etc. The child dreams of becoming a butterfly or an apple. So naturally, the metaphor of foot helps the poet to convey his meaning through an imaginary battle fought between the child’s foot and the surfaces on which the child is likely to walk.

The child’s foot is sure to be hurt when it walks on a street laden with stones and bits of glass and paths in the rough earth and when it climbs the ladder pressing his soft foot on the pointed edges of the rungs of the ladder. Then it realizes that it is a ‘foot’. Here, the poet wants the reader to know that the adult world fights against the spirit of the child and makes him become aware of his role as an individual in human society. At this stage, the foot is imprisoned in a shoe, which means, the child’s consciousness reaches maturity and adulthood.

Adulthood is now represented as ‘adult foot’ enclosed in a shoe. The adult foot gropes in the dark and learns about the harsh realities of life like a blind man. Here, it means, unlike the child’s foot which had more .freedom than the adult’s, the adult foot has to work in a rigid mould given by the society. The ‘shoe’ represents this framework given by society. Here again, the ‘foot’ as a metaphor comes to his help. Therefore, the poet chooses ‘shoe’ as representing societal norms and traditions.

The blind adult foot now walks and works without respite until he dies. The different professions of men are mentioned. The adult foot may be a man’s foot or a woman’s foot and keeps walking through fields, markets, mines, and ministries, and finally toils hard scarcely finding time to enjoy ‘love’ and ‘sleep’. Here also the metaphor of the ‘foot’ facilitates the expression in the line ‘scarcely taking time to bare itself in love or sleep’. Finally, it ceases to be a ‘foot’ when a man chooses to stop working. Thus, the ‘foot’ as a metaphor has been skillfully used by the poet to evoke the right imagery to suit his meaning.

I. Answer the following questions in a word, a phrase, or a sentence each:

Question 1.
What did the foot find when it descended underground?
Everything to be dark (or darkness).

Question 2.
What would like to be a butterfly or an apple in the poem ‘To the Foot from its Child’?
Foot/Child’s foot.

Question 3.
What does the foot do throughout life?
OR
Mention any one of the places through which the foot walks, in ‘To the Foot from its Child’.
Throughout its life, the foot keeps walking without respite. It walks through fields, mines, markets, and ministries until death.

Question 4.
What does the phrase ‘condemned to live in a shoe’ mean?
The phrase ‘condemned to live in a shoe’ means it has to live like other human beings, in human society.

Question 5.
Where did the foot descend after it ceased to be?
It descended underground.

Question 6.
What did the foot find when it descended underground?
When the foot descended underground, it found everything dark there.

Question 7.
What form do the detailed toes of a child take on as they grow?
OR
What form do the petal-like soft toes take inside the shoes?
The petaied toes of a child grow bunched and out of trim, take on the form of eyeless reptiles with triangular heads, like worms.

Question 8.
What do the soft nails of quartz change themselves into?
OR
How do the soft nails of the foot change as the child grows up?
The ‘soft nails of quartz’ in the child’s foot gradually grow hard and change themselves into an opaque substance ‘hard as horn’.

Question 9.
Where is the child’s foot condemned to live?
OR
Where is the defeated foot condemned to live?
The child’s foot is condemned to live in a shoe.

Question 10.
What teaches the foot that it cannot fly?
As the child’s foot grows in time and starts walking on stones and bits of glass, streets, ladders, etc., it learns that it cannot fly.

Question 11.
Where did the foot descend?
The foot descended underground after its death.

Question 12.
What does the foot not realize at the end of the poem?
At the end of the poem, the foot does not realize that it is dead and has ceased to be a foot.

Question 13.
What, according to the speaker, is the child’s foot not yet aware in ‘To the Foot from its Child’.
In ‘To the Foot from its Child’, the child’s foot is not yet aware that it is a foot.

Question 14.
What is out of touch with its fellow in the poem, ‘To the Foot from its Child’?
In the poem, ‘To the Foot from its Child’, the child’s foot is out of touch with its fellow.

Question 15.
Who feels out life like a blind man in the poem, ‘To the Foot from its Child’?
The child’s foot having been imprisoned in a shoe feels out life like a blind man.

Question 16.
What are the toes of the child compared to, in ‘To the Foot from its Child’?
In ‘To the Foot from its Child’, the tiny toes are compared to the petals of a flower.

Question 17.
What does the blind thing refer to, in ‘To the Foot from its Child’?
In ‘To the Foot from its Child’, the blind thing refers to the child’s foot imprisoned in a shoe.

Question 18.
Mention any one of the places through which the foot walks, in ‘To the Foot from its Child’.
In ‘To the Foot from its Child’, the foot walks through markets.

Question 19.
How long does the foot walk, in ‘To the Foot from its Child’?
In ‘To the Foot from its Child’, the foot walks until the whole man chooses to stop and descends underground.

Question 20.
In ‘To the Foot from its Child’, the foot scarcely takes time to bare itself in
(a) rest or peace
(b) love or sleep
(c) death or dream.
(b) love or sleep.

Question 21.
In ‘To the Foot from its Child’, when descending underground, the foot finds everything
(a) dark
(b) rough
(c) coarse.
(a) dark.

Question 22.
In ‘To the Foot from its Child’, the paths in the rough earth go on teaching the foot that it cannot
(a) become a butterfly
(b) bunch together
(c) live in a shoe.
(a) become a butterfly.

II. Answer the following questions in a paragraph of 80-100 words each:

Question 1.
Bring out the contrast between illusion and reality in ‘To the Foot from its Child’.
Pablo Neruda presents his view of ‘life’ using the ‘foot’ as a metaphor for life. He explores life’s experiences as a traveller beginning as a child’s foot until it grows into an adult foot and finally dies. During the course of this journey from life to death as a cycle, the poet tries to delineate man’s ‘dreams’ and how they get crushed in the world by outside forces.

Initially, the infant’s foot is unaware that it is a ‘foot’ and is under the illusion that it can fly like a butterfly or be an apple on a tree. The very same infant’s foot then realizes that it can only serve as a ‘foot’ and it cannot fly like a butterfly or be a fruit. This is the reality. The infant’s foot thus, once it enters the society, is made aware of the reality and it loses its illusions.

Question 2.
Why does the poet refer to the foot’ as being a blind man?
The infant’s foot tries to combat reality and faces stones, streets, bits of glass, ladder, paths in the rough earth, which teach the infant’s foot that it is only a ‘foot’ and they take him ‘prisoner’. The foot gets condemned to live inside a shoe. The shoe here stands for the society, the outside forces which discipline the individual in conformity with the norms and customs of the society. The poet refers to the ‘foot as being a blind man’ because once he is put inside the shoe he loses touch with its fellow and is not free to face reality as he »

Question 3.
Explain how the poet uses a foot as a metaphor for life.
OR
Describe how the foot represents an individual’s life, according to the poem.
In the poem, Neruda uses ‘foot’ as a metaphor for ‘life’. We see different stages in life beginning with infancy or childhood, maturity, adulthood, old age, and finally death. These stages have been delineated in the poem using ‘foot’ as a metaphor. The poem begins with the infant’s foot. Here, like all children, the infant’s foot does not even know that it is only a foot. It has dream-like imagination and aspirations. That is why it dreams of flying like a butterfly with absolute freedom and enjoy the pleasures of life which are expressed as a wish to become an apple.

However, once the child’s foot comes to face the external world, it becomes aware that it is only a ‘foot’ and cannot become a butterfly. Then it matures into an adult and from adulthood grows old and dies.

The poet describes how the child’s foot which has soft, petal-like toes gets transformed into an adult foot which has toes which resemble eyeless reptiles, and are covered with nails which are calloused and bear faint volcanoes of death.

Finally, having become an adult, it slogs throughout life, relentlessly working in fields, markets, mines and ministries without respite and not enjoying the pleasures of life until it dies and is buried. Thus, the ‘foot’ as a metaphor serves the poet to express his view of life.

Question 4.
Why does the foot feel trapped and stifled inside the shoe?
OR
What happens to the foot when it is condemned to live in a shoe?
OR
Bring out the life of the foot in a shoe as presented in ‘To the Foot from its Child’.
The child’s foot is born with a great deal of zest for life and hence it wishes to become an apple on a tree or fly like a bird. But, gradually, as it starts growing, it realizes that it is a ‘foot’ only and cannot become anything else. Then, its spirit loses its battle against the world. It is taken prisoner and is condemned to live in a shoe. Now, having been imprisoned in a shoe, it tries to understand the world, in its own way. It is alone and cannot communicate with its counterpart and gropes blindly in the dark like a blind man. Since it is not in the open, it is not in touch with reality directly.

The society decides what it should understand about ‘life’ or the world outside. Whatever ideas it forms about life have to be formed in the confined space of the shoe. It is here that the child’s spirit becomes aware of its limitations as a human being and understands its role as a social being in human society. That is why it feels trapped and stifled inside the shoe.

Question 5.
Explain the instances that make the child’s foot aware of the obstacles and hardships.
The poem narrates the journey of a child’s foot until it becomes an adult foot and beyond until it dies. The journey of the child’s foot is similar to the ‘journey of life’. The poet personifies ‘foot’ and focuses? his attention on the ‘life’ of man, using the foot as the protagonist. ‘Life’ begins in infancy and so even in this poem, ‘life’ begins as an infant’s foot. It is natural that children, who are naive and innocent, do not know that their foot is meant for walking and it has a function to discharge. But, in its innocence, the child dreams of becoming a butterfly or an apple. Therefore, when the child starts walking on a street laden with stones, and bits of glass and paths in the rough earth, the child’s foot is naturally hurt.

Similarly, when it climbs the ladder pressing his soft foot on the pointed edges of the rungs of the ladder, it is hurt and it realizes that it is a foot. Thus, using the metaphor of ‘foot’, the poet conveys the imaginary battle fought between the individual and the realities of life one has to face in society. At this stage, the foot is imprisoned in a ’shoe’. The ‘shoe’ represents the societal norms and traditions. The ‘blind’ adult foot now walks and works without respite until it dies. The different roles or professions have taken up by an individual in society either as a man or woman are expressed metaphorically in the line:

“up above, down below, through fields, mines, markets, and ministries”.

The individual toils hard, scarcely finding time to enjoy ‘love and sleep’. Here also the metaphor of the ‘foot’ enables the poet to express his ideas as seen in the line:

“Scarcely taking time to bare itself in love or sleep”.

The impact of life’s hardships can be seen in the deformed toes of the child’s foe.. The soft nails of quartz become opaque, are bunched together, and look like eyeless reptiles wit1 triangular heads, grow callused, and are covered with faint volcanoes of death.

Question 6.
How are the contrasting image of a child’s foot and foot confined to a shoe brought out in the poem?
OR
Society crushes childhood dreams and confines them to society and its norms. Explain with reference to the poem ’To the Foot from its Child’.
OR
Explain how the foot toils in its shoe until the whole man chooses to stop in ‘To the Foot from its Child’.
The child’s foot is naive, and innocent and not yet aware that it is only a foot. That is why it wishes to be a butterfly or an apple. But, as the foot grows, it starts walking and it trods on stones, bits of glass, streets, ladders, and the paths in the rough earth. It soon realizes that it is only a ‘foot’ and it cannot fly or cannot become a bulging apple on a tree. It loses its state of innocence. Its spirit gets crushed and is defeated in realizing its aspirations.

With this awareness and maturity, the child’s foot gets imprisoned in a shoe and gradually attains adulthood. Unlike a child, an adult cannot live as he/she likes. He/She has to live as a member of the society which imposes its own rigid framework on the individual. The shoe symbolizes societal norms and traditions. Inside the shoe, it tries to understand the world alone in isolation. It serves as the foot of a man or woman working in the fields, or market or mines or ministries and toils hard day and night until it dies. The poet wishes to say that the freedom of childhood is lost when a person becomes an adult and faces a life of constant work and struggle.

The impact of this life of struggle and hardships is seen in the differences one notices in a child’s foot and the foot of an adult. The soft nails of quartz seen in an infant’s foot become opaque, are bunched together, and look like eyeless reptiles with triangular heads, grow callused, and are covered with faint volcanoes of death.

Question 7.
How does the poet describe the monotonous life of the individual confined in a shoe?
OR
How does the poem ‘To the Foot from its Child’ bring out the plight of a person dictated by
society?
It is natural that children, who are naive and innocent, do not know that their foot is meant for walking and the ‘foot’ has a function to discharge. Through the use of the ‘foot’ as a metaphor, the poet cleverly brings out the battle between harsh realities of life symbolically expressed as stones, streets, ladder, bits of glass, etc. The child dreams of becoming a butterfly or an apple. So naturally, the metaphor of foot helps the poet to convey his meaning through an imaginary battle fought between the child’s foot and the surfaces on which the child is likely to walk.

The child’s foot is sure to be hurt when it walks on a street laden with stones and bits of glass and paths in the rough earth and when it climbs the ladder pressing his soft foot on the pointed edges of the rungs of the ladder. Then it realizes that it is a ‘foot’. Here, the poet wants the reader to know that the adult world fights against the spirit of the child and makes him become aware of his role as an individual in human society.

At this stage, the foot is imprisoned in a shoe, which means, the child’s consciousness reaches maturity and adulthood. Adulthood is now represented as ‘adult foot’ enclosed in a shoe. The adult foot gropes in the dark and learns about the harsh realities of life like a blind man. Here, it means, unlike the child’s foot which had more freedom than the adult’s, the adult foot has to work in a rigid mould given by the society. The ‘shoe’ represents this framework given by society. Here again, the ‘foot’ as a metaphor comes to his help. Therefore, the poet chooses ‘shoe’ as representing societal norms and traditions.

The blind adult foot now walks and works without respite until he dies. The different professions of men are mentioned. The adult foot may be a man’s foot or a woman’s foot and keeps walking through fields, markets, mines, and ministries, and finally toils hard scarcely finding time to enjoy ‘love’ and ‘sleep’. Here also the metaphor of the ‘foot’ facilitates the expression in the line ‘scarcely taking time to bare itself in love or sleep’. Finally, it ceases to be a ‘foot’ when a man chooses to stop working. Thus, the ‘foot’ as a metaphor has been skillfully used by the poet to evoke the right imagery to suit his meaning.

Question 8.
Trace the stages of the foot’s transformation as portrayed in ‘To the Foot from its Child’.
OR
Bring out the changes that the foot undergoes after being condemned to live in a shoo-in ‘To the Foot from its Child’.
‘To the Foot from its Child’ narrates the journey of a child’s foot until it becomes an adult foot and beyond until it dies.

In the first stanza, there are only two lines which express the innocence of the child and its wishes. The child wants to be a butterfly or an apple, but society is harsh and forces the child to become a responsible adult doing responsible adult things.

In the next stanza, the child’s foot walks in the real world and experiences the harsh realities of life. The words, ‘stones, bits of glass, streets, ladders, paths in the rough surface of the earth’ symbolize the forces in society.

When the child’s foot encounters them in a battle, it learns that its role is that of a foot only and it cannot become a butterfly or an apple. The foot is now imprisoned in a shoe, where it grows into an adult. It gets exposed to reality as filtered through the shoe. It suffers loneliness and gradually learns the realities of life groping in the dark like a blind man.

During this life inside the shoe, it loses all the beauty of a child’s foot. Its soft, nice, petal-like toes lose their beauty, become hard, callused, and look like eyeless reptiles.

The ‘foot’, now has grown into an adult foot, keeps on walking, works without respite in fields, markets, mines, and ministries. It toils hard giving up all its worldly pleasures and finally dies. It is then buried. But, as it descends into the ground, it loses its human awareness and does not know that it is not even a foot. So, in its spirit, it is like the child’s foot and dreams of becoming a butterfly or an apple.

Thus, the poet depicts his view of life in the metaphor of a foot, with a clear progression from infancy, to maturity, to adulthood, old age, and finally death.

Question 1.
The poem ‘To the Foot from its Child’ depicts the progression from childhood through adulthood to old age and finally, death. Discuss.
OR
The poem ‘To the Foot from its Child’ is a comment on the journey of human life. Elucidate.
OR
Trace the stages of the foot’s transformation as portrayed in ‘To the Foot from its Child’.
In the poem ‘To the Foot from its Child’, Pablo Neruda expresses his view of life using the metaphor of ‘foot’. The poem begins with a description of the child’s naivety. The child’s foot does not know that it is a foot. It dreams of unlimited possibilities. It wants to become a butterfly enjoying unbridled freedom and enjoying the pleasures of life symbolized by the apple.

The poet expresses the experience of the child’s foot when it is exposed to reality in the real world. It walks over stones, streets, ladders, bits of glass, paths in the rough surface of the earth. All these symbolically stand for obstacles, problems, difficulties, and hurdles that one encounters in real life. When the child’s foot faces these realities, it attempts to fight them, and it becomes aware that it was in an illusory world and it does not have infinite possibilities in life but has to serve as a foot only.

It is also convinced that it cannot become a butterfly or an apple. The outside forces capture him and he is imprisoned in a shoe. Now, from that of an infant’s foot, it has grown to be an adult and now the adult has been forced to live like any human individual.

Then, we get a description of the changes that the child’s foot undergoes inside the shoe. Its nice, soft, petal-like toes lose their ‘lustre’ and the nails become harder, the toes grow bunched and look like eyeless reptiles, grow callused and are covered with faint volcanoes of death. Inside the shoe, the adult foot is like a blind man groping in the dark. This state depicts the helplessness of man when he faces the harsh realities of life as a member of society.

He slogs without respite and keeps on walking, until his death. He works in fields, markets, mines, and ministries either as a man’s or a woman’s foot. He does not find time to enjoy his rightful pleasures of life like ‘love’ and ‘sleep’. Finally, one day the foot ceases to walk when the man dies.

When he is buried the foot goes underground. But now he does not know that he is no longer a ‘foot’. In his consciousness, he is equal to the child’s consciousness and hence he again dreams of becoming a butterfly or an apple. Thus, the poet depicts his view of life, tracing its characteristics through different stages like infancy, reaching maturity, adulthood, old age, and finally death. Thus, the poem also brings out a cyclical view of life – birth, infancy, maturity, adulthood, old age, death, and rebirth.

Question 2.
Describe the various stages that the foot goes through and what the foot learns and how it changes at each stage.
In the poem ‘To the Foot from its Child’, Pablo Neruda expresses his view of life using the metaphor of ‘foot’. The poem begins with a description of the child’s naivety. The child’s foot does not know that it is a foot. It dreams of unlimited possibilities. It wants to become a butterfly enjoying unbridled freedom and enjoying the pleasures of life symbolized by the apple.

The poet expresses the experience of the child’s foot when it is exposed to reality in the real world. It walks over stones, streets, ladders, bits of glass, paths in the rough surface of the earth. All these symbolically stand for obstacles, problems, difficulties, and hurdles that one encounters in real life. When the child’s foot faces these realities, it attempts to fight them, and it becomes aware that it was in an illusory world and it does not have infinite possibilities in life but has to serve as a foot only. It is also convinced that it cannot become a butterfly or an apple. The outside forces capture him and he is imprisoned in a shoe. Now, from that of an infant’s foot, it has grown to be an adult and now the adult has been forced to live like any human individual.

Then, we get a description of the changes that the child’s foot undergoes inside the shoe. Its nice, soft, petal-like toes lose their ‘lustre’ and the nails become harder, the toes grow bunched and look like eyeless reptiles, grow callused and are covered with faint volcanoes of death. Inside the shoe, the adult foot is like a blind man groping in the dark. This state depicts the helplessness of man when he faces the harsh realities of life as a member of society. He slogs without respite and keeps on walking, until his death. He works in fields, markets, mines, and ministries either as a man’s or a woman’s foot. He does not find time to enjoy his rightful pleasures of life like ‘love’ and ‘sleep’. Finally, one day the foot ceases to walk when the man dies.

When he is buried the foot goes underground. But now he does not know that he is no longer a ‘foot’. In his consciousness, he is equal to the child’s consciousness and hence he again dreams of becoming a butterfly or an apple. Thus, the poet depicts his view of life, tracing its characteristics through different stages like infancy, reaching maturity, adulthood, old age, and finally death. Thus, the poem also brings out a cyclical view of life – birth, infancy, maturity, adulthood, old age, death, and rebirth.

Question 3.
Bring out the stages of hardships faced by the foot after being confined in a shoe.
OR
Explain the various stages of hardships faced by the foot after being confined in a shoe.
OR
Describe the different stages of transformation of the foot after it is condemned to live in a shoe.
OR
The foot is forced to play various roles and shoulder many responsibilities. Explain with reference to ‘To the Foot from its Child’.
As the child learns to walk and starts walking on stones, bits of glass, streets, ladders and the rough surface of the earth, the child’s foot becomes aware of its role. It learns that it is a foot and cannot become a butterfly or a bulging fruit on a tree. Once it realizes that it is a foot, it is defeated in realizing its aspirations and gets imprisoned in a shoe. Inside the shoe, it tries to understand the world in its own way, alone, like a blind man groping in the dark. During this period its soft nails of quartz become opaque, are bunched together, and look like eyeless reptiles with triangular heads, grow callused, and are covered with faint volcanoes of death.

These changes happen because, once the child’s foot becomes an adult’s foot, it walks as the foot of a man or woman and keeps walking in the fields as a farmer, or as a grocer in the markets, or as a miner in the mines or as a church minister or a government worker, until its death. Thus, the foot experiences the hardships of life and loses its ‘soft’ and flowery petal-like form.

Question 4.
“The norms of the social control a man just as the foot is enclosed in a shoe”. How is this depicted in ‘To the Foot from its Child’?
The poet Neruda uses the ‘foot’ as a metaphor and conveys his view of life. Thus, by personifying the foot, the poet expects the readers to compare the experience of the foot to the whole person’s hopes and dreams as well as to the realities of everyday life. By and large, one can say that the poem is basically a criticism of how people force children to grow in society forgetting all their dreams and aspirations. The child wants to be a butterfly or an apple, but society is harsh and forces the child to become a responsible adult doing responsible adult things.

As a child’s foot, it has relatively more freedom than the adult’s foot. As the infant’s foot starts walking in the real world outside, it steps over “stones and bits of glass, streets, ladders and the paths in the rough earth’’. It realizes that its role is that of a foot and it cannot become a butterfly or an apple. The moment it discovers that it is only a foot, its spirit loses its battle against the world. It surrenders itself to the dictates of the society. It is taken prisoner and is condemned to live in a shoe.

It also means that the child’s spirit becomes aware of its limitations as a human being and understands its roles, duties, and responsibilities as a social being in human society. It is true that “the foot is a symbol for the helplessness of an individual in the vice-like grip of an insensitive system”. This meaning is captured in the phrase ‘condemned to live in a shoe’. Once it gets imprisoned, it has to slog there until it dies. The society decides what it should understand about ‘life’ or the world outside. Gradually, the foot adapts itself to its world and learns to cope with the harsh realities of life.

The adult foot gets trapped in the routines of everyday life or the humdrum commonality of existence. It is now less capable of enjoyment and finds life difficult in every walk of life. It slogs and slogs either as a man’s foot or as a woman’s foot working in the field or market or mines or ministries day and night, scarcely finding time to enjoy the pleasure of love or sleep. It works without respite and finally meets with death.

To the Foot from its Child by Pablo Neruda About the Poet:

Pablo Neruda (1904-1973) is the pen name and, later legal name of the Chilean poet, diplomat, and politician Ricardo Eliecer Neftali Reyes Basoalto. In 1971 Neruda won the Nobel Prize for Literature.

Neruda became known as a poet while still a teenager. He wrote in a variety of styles including surrealist poems, historical epics, overtly political manifestos, a prose autobiography, and erotically- charged love poems such as the ones in his 1924 collection ‘Twenty Love Poems and a Song of Despair’.

Neruda’s poetry is renowned for its fantastic imagery and surreal use of language. The surrealists attempted to express in art and literature the workings of the unconscious mind and to synthesize. these workings with the conscious mind.

Neruda believes that our most intense experience of impermanence is not death, but our own isolation among the living. It is probably this idea that gets reflected in the poem ‘To the Foot from its Child’. According to Neruda, “it was through metaphor, not rational analysis and argument, that the mysteries of the world could be revealed”.

Background:

‘To the Foot from its Child’ is the translated English version of the original poem ‘Al Pie Desde Su Nino’ written by Pablo Neruda and translated into English by Alastair Reid. [The poem appears in the collection of poems titled ‘Estravagaris’ published in 1958. ‘Extravagaris’ (Book of Vagaries) is the English title given by Reid].

To the Foot from its Child Summary in English

‘To the Foot from its Child’ by Pablo Neruda is a narrative-descriptive poem which narrates the journey of a child’s foot until it becomes an adult foot and beyond until it dies. Besides narrating the experiences of the adult foot until its death, the poem also describes the changes that the child’s foot undergoes until it becomes an adult foot.

The journey of the child’s foot is similar to the ‘journey of life’. The poet uses the ‘foot’ as a metaphor and conveys his view of life. This metaphor helps the poet to convey the idea of how the child’s spirit gets crushed through the challenges and restrictions that life places upon him. Thus, by personifying the foot, the poet expects the reader to compare the experience of the foot to the whole person’s hopes and dreams as well as to the realities of everyday life. By and large one can infer that the poem is basically a criticism of how people force children to grow in society and forget all their dreams and aspirations. The child wants to be a butterfly or an apple, but society is harsh and forces the kid to become a responsible adult doing responsible adult things.

The transition of the child’s foot into an adult foot and then until its death can be studied under four stages conveniently. The four stages are

1. Childhood
2. Experiencing Reality
3. Maturity and
4. Death and Rebirth.

A brief description of each stage is given below:

1. Childhood (Lines 1 – 2):
The first stanza describes the characteristic features of the child’s foot. It is an infant’s foot and it does not know that it is a ‘foot’ at all. It lacks awareness and hence it dreams of unlimited possibilities. It would like to be a ‘butterfly’ or an ‘apple’. The foot has an optimistic view of life.

2. Experiencing Reality (Lines 3 – 16):
Here the poet highlights the impact of time on the child. As the infant’s foot starts growing in the outside world, it begins to experience the harshness and pain of life while walking. When it steps over, “stones and bits of glass, / streets, ladders / and the paths in the rough earth, it learns that its role is that of a foot the same way people become aware of their role in life. It realizes that it can neither fly like a butterfly nor become a bulged apple on the branch of a tree. The child’s foot has now discovered that it is only a ‘foot’, its spirit loses its battle against the world, is taken prisoner, and is condemned to live in a shoe. It also means that the child’s spirit becomes aware of its limitations as a human being and understands its role as a social being in human society.

Now, having been imprisoned in a shoe, it gradually tries to understand the world, in its own way. It is alone and cannot communicate with its counterpart, and gropes blindly in the dark like a blind man. The ‘foot’ is not in the open and whatever ideas it forms about life, are formed in the confined space of the shoe. Here, it means, it is not in touch with reality directly. The society decides what it should understand about ‘life’ or the world outside. Gradually, the foot adapts itself to its world and learns to cope with the harsh realities of life.

3. Maturity (Lines 17 – 46):
In this part of the poem the poet gives a graphic description of the changes seen in the child’s foot during its transition from a child’s foot to ‘adult foot’. The ‘soft nails of quartz’ in the child’s foot gradually grow hard and change themselves into an ‘opaque’ substance ‘hard as horn’. The ‘tiny petaled toes’ of the child’s foot ‘grow bunched and out of trim’. The toes in the adult foot appear like ‘eyeless reptiles’. Later they grow harder and become callused.

In this stanza, the poet attempts to let the reader know that as the child grows into an adult it becomes less open to reality. It also means that people grow harder both physically and emotionally. The phrase ‘faint volcanoes of death’ suggests that the foot comes to appreciate ‘mortality’. Thus, we find that the child’s foot has now been transformed from a beautiful form into a warped and ugly one.

The poet then describes the journey of an adult foot until its death. It is now like an eyeless reptile. Hence he calls it a ‘blind thing’. The adult foot is now in the harsh world outside, suggesting that the adult gets trapped in the routines of everyday life or the humdrum commonality of existence. It is now less capable of enjoyment and finds life difficult in every walk of life. It slogs and slogs either as a man’s foot or as a woman’s foot working in the field or market or mines or ministries. It toils in the shoe, day and night, scarcely finding time to enjoy the pleasures of life or sleep. It works without respite and finally meets with death.

4. Death and Rebirth (Lines 47 – 53):
Soon after the death, the adult foot gets buried. It goes down into the underground. It finds everything dark there. It also does not know that it is dead and has ceased to be a foot. When the foot dies and is buried, its consciousness is childlike again. Therefore, the foot revisits the possibilities of flying like a butterfly or becoming an apple. Here it means that people consider the possibility of an after-life.

To sum up, the freedom of childhood is lost when a person becomes an adult and is exposed to a life of constant work and struggle. Outside, uncontrollable forces have the power to direct one’s life and thus ‘life’ in society takes away people’s free spirits until they are freed again by death. The human promise is not fulfilled by those whom society enslaves and mistreats.

The poet imagines that the naked foot of a boy, innocent still of the habituations of social society does not know that it is a foot, or a butterfly or an apple.

Only through a long process of denial of our embodied natures, beginning with the simple act of wearing shoes and thus denying contact with the earth does the boy become a man. However, upon being buried, he still does not know if he will fly or become an apple.

To the Foot from its Child Summary in Kannada

Glossary:

• Quartz: a hard white colourless mineral consisting of silicon dioxide
• Opaque: not transparent
• Petaled: like petals
• Callus: thickened and hardened part of the skin
• Respite: a short period of rest

Karnataka 2nd PUC Economics Question Bank Chapter 4 Production and Cost

2nd PUC Economics Production and Cost One Mark Questions and Answers

I. Answer the following in a sentence each.

Question 1.
What do you mean by production?
Production is the process in which transformation of inputs into output takes place. Here inputs are converted into output. For example, raw cotton is made into cloth.

Question 2.
Define Production function.
According to Watson, Production function is “the relationship between physical inputs and physical output of a firm”.

Question 3.
What is Total Product?
Total product refers to total volume of goods and services produced by a firm during a specified period of time.

Question 4:
What is Average Product?
The Average product refers to per unit of output produced with the help of variable factor.

Question 5:
Define Marginal Product.
The Marginal Product refers to additional unit of output produced with help of additional factor input.

The Postive Factors of 70 are therefore all the numbers we used to divide (divisors) above to get an even number.

Question 6.
Define Iso-quant.
An Iso-quant is a curve on which the various combinations of labour and capital show the same level of output. It also refers to the locus of all possible combinations of two inputs (Labour and Capital) which result in the same output level.

Question 7.
What do you mean by cost?
Cost of production refers to the expenses incurred by the producer to produce various goods and services. It includes all those expenditures incurred by a firm or industry to manufacture their products.

Question 8:
What is Fixed cost?
Ans. These are the costs which are incurred on fixed factors of production. The amount of expenditure.spent on fixed factors is unaltered in the short run.

Question 9.
What is Variable cost?
Variable costs are the expenses incurred on the variable inputs like raw materials, ordinary labourers, electricity etc.

Question 10.
Define Total cost.
It is the aggregate money expenditure incurred by the firm on all the factors to produce a given quantity of output.

Question 11.
What is Average variable cost?
It is a variable cost for per unit of output. It can be calculated by dividing total variable cost by the total units of output.

Question 12:
What is average cost?
It is the cost per unit of output produced. It is obtained by dividing total cost by the total output produced, i.e. AC = TC/output.

Question 13:
Define Marginal cost.
Ans. It is an additional cost incurred to produce an additional output. In other words it is the net additions to the total cost when one more unit of output is produced. MC = TCn – TCn-1,

Question 14.
What is the shape of MC and AC curves?
The shape of AC and MC is ‘U’ shaped and can be represented as follows:

Question 15.
Who introduced the concept of Real cost?
Prof. Alfred Marshall introduced the concept of Real cost.

2nd PUC Economics Production and Cost Two Marks Questions and Answers

Question 1.
Write the production function in the form of an equation.
The production function can be written as follows:
Q = f(R, L, K, O…..) where Q is quantity produced, f is function, R refers to Land, L to labour K to capital, O to organization.

Question 2:
If 4 units of labour produce 70 units of‘x’and 5 units of labour produce 75 units of ‘x’, calculate Marginal product and Average product.
Calculation of Marginal product:
4 Labour – 70 Units of ‘x’
5 Labour- 75 Units of ‘x’
MP = TPn -TPn-1 , where TPn= 75,  TPn-1=70
= 75 – 70
= 5 units of product.
So, MP = 5

Calculation of Average Product (AP):
AP = TP/Input(Labour)
4 Labour – 70 Units of ‘x’
AP = 70/4 =17.5 with 4 labourers and capital
5 Labour- 75 Units of ‘x’
AP = 75/5 = 15 with 5 labourers and capital

Question 3.
Why are Average and Marginal Cost curves ‘U’ shaped.
For an increase in the output, AC and MC fall initially then reach a minimum value and later rise with the rise in output. The change in MC is greater than that in AC.

In the beginning, AC falls due to the more influence of of AFC and later rises under the influence of AVC with an increase in output. This makes AC to become U shaped.

MC falls as output increases in the beginning. It starts rising after a certain level of output. This happens because of the influence of the law of variable proportions. The fact that Marginal Product rises first, reaches maximum and then declines ensures that the Marginal Cost curve of a firm declines first, reaches minimum and then rises and becomes U shaped.

Question 4.
Mention the three laws of variable proportions. .
The three laws of Variable Proportions are as follows:

1. The law of Increasing Returns.
2. The law of Diminishing Returns.
3. The Law of Negative Returns.

Question 5.
Write the meaning of increasing returns.
When the output increases in a greater proportion than the increase in inputs it is called as Increasing Returns. When a firm expands, increasing returns to scale are obtained in the beginning. Here the Total Product increases at increasing rate, For example, if there is 20% increase in inputs, the output increases by 30%.

Question 6.
Give the meaning of diminishing returns.
Also known as decreasing returns to scale, operates when output increases in a smaller proportion for an increase in all inputs. Here, the Total Product increases in a decreasing rate. For example, if a producer increases all inputs by 20%, the total product may increase by 15% only.

Question 7.
Mention any four short run costs:
The four major short run costs are as follows:

1. Fixed Cost
2. Variable Cost
3. Total Cost
4. Average Cost.

Question 8.
Mention the costs involved in the long run.
In the long run, we have three types of costs viz.., Total cost, Long run average cost, and Long run marginal cost.

Question 9.
Why does the SMC cut SAVC at its minimum point? .
When the Short run Average Variable Cost (SAVC) is decreasing, the Short run Marginal Cost (SMC) also should decrease and when SAVC increases, the SMC should also increase but more than SAVC. Hence, the SMC curve has to cut SAVC from below at the minimum point.

Question 10.
What is Opportunity cost?
It is the cost of the next best alternative product which is measured in terms of revenue earned by the factor when it is employed in other alternative jobs.

In other words it is the cost of displaced alternative. While calculating opportunity cost the profit earned from the best alternative employment sacrificed is taken into consideration.
The concept of opportunity cost was popularized by an American writer -Prof.Heberlour.

2nd PUC Economics Production and Cost Five Marks Questions and Answers

Question 1.
Explain the concepts of Total Product, Average Product and Marginal Product with the help of a diagram:
(i) Total Product (TP): It refers to the aggregate output produced with the help of factor inputs during a particular period of time. It is obtained by adding the Marginal product contributed by each input.

(ii) Average Product(AP): Average product is an unit of output which is produced per unit input. It is calculated by dividing the Total Product by the variable inputs.

AP = $$\frac{\mathrm{TP}}{\mathrm{L}}$$
where TP is Total product and L variable factor input (e.g. Labour)

(iii) Marginal Product (MP): Marginal product refers to additional unit of output produced with the help of additional unit of input of labour or Capital. We can calculate MP with the help of the following formula:
MP = TPn – TPn-1

Where, MP is marginal product, TPn is Total product of‘n’ units, and TPn-1 is Total product of the previous unit of output.
Diagrammatic representation of TP, AP and MP.

The total product (TP) curve, in the beginning increases at increasing rate later at decreasing rate, reaches maximum and starts falling.

The average product (AP) curve rises in the beginning, reaches maximum with the increase in inputs and output. The marginal product (MP) rises, reaches maximum level before AP and falls. It becomes zero when TP is maximum. When TP starts falling the MP curve crosses ‘x’ axis to become negative.

Question 2.
Explain the law of variable proportions. (LVP)
The LVP refers to input-output relationship, when the output is increased by varying the quantity of one input. This law operates in short period when all the factors of production cannot be increased or decreased simultaneously. The producer can enhance the output by increasing only one variable input by keeping other factors fixed. So, there will be change in proportion between Variable and Fixed Inputs. This is called as the Law of Variable proportions.

Assumptions of LVP:

• The LVP operates under certain assumptions: They are:
• The technique of production remains same.
• There will be existence of Fixed inputs.
• The efficiency of variable inputs will be equal.
• There is possibility to change the proportion of inputs.
• The factor inputs are not close or perfect substitutes.

The law states that, an increase in variable inputs, in a given state of technology, cause output to increase, but after a point the extra output resulting from the same addition of extra inputs will become less and less.

The LVP can be illustrated with the help of a table:

In the above table, the producer (farmer) has 5 hectares of land in which he has spent Rs.25,000 for Agricultural machineries. When he increases labour input the TP, AP and MP increase in the beginning and later diminish. When the producer applies 3 units of labour the MP is highest at 30. Till here, the TP is in increasing returns. From 4th unit of labour, the MP and AP start decreasing. At 7th unit of labour the MP becomes zero indicating that the TP has reached optimum. When the producer uses 8th labour the MP becomes negative and TP starts falling.

Stages of LVP:
There are three stages of production as per LVP (i) Increasing Returns (2) Diminishing Returns and (3) Negative Returns.

I Stage-Increasing Returns:
In this stage, TP increases at an increasing rate i.e., up to 3rd unit of labour, MP also rises and reaches maximum at this point and AP also goes on increasing.

Causes for Increasing Returns: The law of increasing returns operates because, in the beginning the quantity of fixed factors is abundant relative to the quantity of the variable factor. When the producer adds more units of variable input to the fixed factor of inputs, then the fixed factors are more intensively and effectively used. That means the efficiency of the fixed factors increase as additional units of the variable factors are added to it.

Another reason for increasing returns during first stage is that as more units of variable factors are employed, the efficiency of the variable factors itself increases. This is because with sufficient quantity of variable factor, introduction of division of labour and specialization becomes possible which leads to increase in output.

II Stage – Diminishing Returns: .
In this stage, the TP continues to increase at a diminishing rate till it reaches 95 tons. Here, both AP and MP fall but they are positive. At the end of this stage, the MP becomes zero. This stage is called diminishing returns as both AP and MP start decreasing with the increase in inputs.

Causes for diminishing returns: When the producer increases the variable inputs even after the point where the variable input is sufficient to ensure efficient utilisation of the fixed factor, then further increase in the Variable factor will cause MP and AP to decline. This is because the fixed factor becomes inadequate relative to the quantity of variable factor.

Another reason for diminishing returns is the imperfect substitutability of one factor for another. If there is perfect substitute of the scarce fixed factor is available, the second stage would have been made up by increasing the supply of its perfect substitute with the result that output could be expanded.

III Stage – Negative Returns:
During the 3rd stage, the TP and AP will be falling and MP is negative. It is called negative returns as MP is negative.

Causes for negative returns: When the producer increases labour input beyond 6 units, the TP declines and MP becomes negative. This is due to the fact that’the quantity of variable factor becomes too excessive in relation to the fixed factor so that they get in each other’s ways which result in decline in TP. In such situation, the producer has to reduce variable inputs to reduce the pressure on fixed factor.

Stage of operation-Production: Now the major question is which stage a rational producer , will seek to produce? A rational producer will never produce in 3rd stage where MP is negative. The producer will also do not produce in first stage where the MP is increasing which is beneficial. If the producer selects to produce at first stage, he will not be making best use of the fixed factor and he will not be utilizing fully the opportunities of increasing production by increasing quantity of the variable factor whose AP continues to rise throughout the first stage.

Thus, a rational producer will never produce in stages I and III. These stages are economic nonsense. Hence he selects the II stage to produce.

The LVP can be represented in the following diagram:

In the above diagram, factor input labour is measured in OX axis and TP, AP and MP are measured on OY axis. In the first stage, the producer is producing RS of output with OS level of variable input. During this stage, TP, AP and MP are increasing,

When the producer increases input labour from OS to OU, the TP reaches maximum at TU in the second stage. Here TP curve is increasing but MP and AP curves are decreasing and MP reaches zero at point U. In the third stage, the TP, AP and MP are falling and MP becomes negative. Here, the TP falls from T and AP remains positive though it is falling.

Question 3.
Explain the laws of returns to scale with the help of a diagram. .
We know that, in the long run all factor inputs are variable. The returns to scale explain the relationship between input and output in the long period. They study about the changes in output as a consequence of changes in all the inputs. This can be represented as follows:
Q = f (X1,X2,……..)

Stages of Returns to Scale: Returns to scale may be (1) Increasing Returns to Scale, (2) Constant Returns to Scale (3) Diminishing Returns to Scale.
These returns to scale can be seen in Total Product which is the result of changes in all inputs.

1. Increasing Returns to Scale: Here, the output increases in a greater proportion than the increase in inputs. When a firm expands, increasing returns to scale are obtained in the beginning. For example, if there is 20% increase in inputs, the output increases by 30%. The increasing returns to scale also is a result of indivisibility of factors. Some factors are available in large and can be utilized with utmost efficiency at a large output.

2. Constant Returns to Scale: The constant returns to scale exists when the output increases in same proportion with the increase in inputs. For example, if a producer increase inputs by 25%, the Total product increases by 25%. Here the Total Product increases at constant rate. It has been found that an individual firm passes through a long phase of constant returns to scale in its lifetime.

3. Diminishing Returns to Scale: Also known as decreasing returns to scale operate when output increase in a smaller proportion with an increase in all inputs. For example, if a producer increases all inputs by 20%, the Total product increase in 15%. Diminishing returns to scale eventually occur because of increasing difficulties of management, coordination and control. When the firm has expanded to a very large size it is difficult to manage it with same efficiency as earlier. So, the dimininishing returns to scale exist.

The returns to scale can be illustrated with the help of the table given below:

 Factor inputs (L+C) Total Product Marginal Product Returns to Scale 1+2 2+4 3+6 10 30 60 10 20 30 Increasing Returns    to Scale 4+8 5+2 6+12 100 140 180 40 40 40 Constant Returns     to Scale 7+14 8+16 9+18 210 230 240 30 20 10 Decreasing Returns to Scale

In the above table, we can notice that the Total product is increasing at increasing rate (MP is increasing by 10, 20, 30, 40) with the increase in both the inputs Labour and Capital (L+C). If the producer increases the inputs any further, TP increases at constant rate (MP is constant at 40). Later, the TP increases at diminishing rate causing decreasing returns to scale (MP starts falling from 40, 30, 20, 10).

The laws of returns to scale can be graphically explained with the help of the following diagram:

In the above diagram, inputs are measured along ‘OX’ axis, Marginal product is measured along ‘OY’ axis. From point P to Q, it is increasing returns, from Q to R it is constant returns and from R to S it is decreasing returns to scale.

Question 4.
Discuss the various types of short run costs.
1. Total Fixed Cost (TFC): It refers to the total money expenses incurred on all the fixed factors in the short run. TFC remains constant at all levels of output. Therefore the total fixed cost curve is a horizontal straight line parallel to ‘X’ axis above the origin which indicates that it is never zero. This can be represented as follows:

TFC = TC-TVC

2. Total Variable Cost (TVC): It refers to the total money expenses incurred on the variable factor inputs in the short-run. Total variable cost is the direct cost of the output because it increases along with the output and remains zero when the output is zero. So, the TVC curves starts from the origin and rises sharply in the beginning, gradually in the middle and stretch again sharply in the end. The nature of this slope is in accordance with the law of variable proportion. This can be represented as follows: –

The Total Variable Cost is obtained as follows:
TVC = TC – TFC

3. Total Cost (TC): It is the aggregate money expenditure incurred by the firm on all the factors to produce a given quantity of output. TC varies in the same proportion as total variable cost because the total fixed cost is constant. The TC curve slope upwards from left to right, above the origin, indicating that, it includes total fixed cost and total, variable cost. This can be represented as follows:

4. Average Fixed Cost (AFC): It is the fixed cost per unit of output. In other words, it is average expenses incurred on a single unit of output produced. AFC and output are in inverse relation i.e., AFC will be higher when the output level is less and as the output goes on increasing AFC starts reducing. When represented in a diagram, AFC curve will have a negative slope which falls very stiffly in the beginning and later on becomes parallel to the X axis. This shows that it is never zero as TFC is never zero. This can be represented as follows:

5. Average Variable Cost (AVC): It is a variable cost per unit of output. It can be calculated by dividing total variable cost by the total units of output. When this cost is graphically represented, we get a ‘U’ shaped AVC, which shows that the cost will be less as the number of units produced increases. This is because as the number of variable inputs are added in a fixed plant the efficiency will increase and vice versa. This can be represented as follows: .

AVC = TVC/output or AVC = AC – AFC

6. Average Cost (AC): It is the cost per unit of output produced. It is obtained by dividing total cost by the total output produced i.e. AC = TC/Q or it is also obtained by adding AFC and AVC. If the AC is graphical represented we get U shaped curve because of the operation of law of variable proportions. The short run AC curve is also called as ‘Plant Curves’ because it indicates the optimum utilization of a given plant (Industry) capacity.

7. Marginal Cost (MC): It is an additional cost incurred to produce an additional output. In other words it is the net additions to the total cost when one more unit of output is produced. MC = TCn – TCn-1

Where TCn = Total cost of ‘n’ selected units of output and TCn-1 is total cost of the previous output

Question 5.
Explain long run costs with the help of a diagram
Long run is defined as a period of time where adjustment to changed conditions is possible. During this period, the size of the plant can be changed at both fixed and variable factors. As all the factors are variable, the total cost constituents completely become total variable cost.

Long Run Average Cost:
It is per unit cost of production of different levels of output. It Is derived by dividing long run total cost from the total level of output.

The long run cost mid output relation is explained by drawing the long run cost curve through short run cost curve. This is because the long period is made up of many short periods which are shown as follows:

In the above diagram LAC curve is a drawn on the basis of 3 possible plant sizes and there are short run average cost curve such as SAC1, SAC2, and SAC3. They represent 3 different sales of output. For the output OQ the average cost will be LQ in the short run as well as long run.

Thus the diagram above shows that the cost incurred in the long run will be lesser than that of the short run. Therefore LAC curve is described as the planning curve which helps in producing optimum level of output at the minimum average cost. LAC is also called as Envelope curve because it includes a group of SAC curves which indicate different levels of output.

Long Run Marginal Cost: The concept of Marginal Cost in the long run is as that of LAC. The LMC curve is also derived from short run Marginal cost curves. The LAC and LMC are U shaped and more flatter than short run AC and MC. The LMC cuts LAC from below where LAC is at minimum. Both LAC and LMC are U shaped because of operation of law of returns to scale.

Question 6.
Explain the various economies and dis economies of scale.
(i) Internal Economies: The internal economies (advantages of large scale production) arise within the firm when it increases its scale production by increasing all inputs. The major internal economies are as follows:

• Technical economies – benefits from capital equipment i.e., machines
• Managerial economies – reduction in managerial expenses
• Marketing economies – can manage bulk orders of supply
• Financial economies – can easily raise finance/loan.
• Risk bearing economies – can face ups and downs in business.
• Transport and storage economies – development of transport and warehouse of its own.

(ii) External Economies: These are the benefits which a firm gets when the entire industry is expanded. They accrue to all the firms as a result of expansion in the output of whole industry and they are not dependent on the output level of individual firms. The firms get these economies from outside because of expansion of the industry. The major external economies are as follows:

• Low cost of raw materials and capital equipments.
• Technological economies-use of latest techniques of production.
• Development of skilled labour – trained labour for higher productivity. .
• Growth of ancillary industry – small scale industries to supply spare parts and use of by-products.
• Development of Transportation, communication and marketing facilities.

(iii) Diseconomies and Decreasing Returns to scale:
The decreasing returns in the production process operate mainly because of diseconomies of large scale production. The firm faces lots of difficulties in managing these roadblocks. When the size of the firm is expanded, its management and supervision becomes, complicated. There are many disadvantages of large scale production which area also known as dis-economies of scale.

There are two types of diseconomies viz., Internal Diseconomies and External Diseconomies of scale.

(a) Internal Diseconomies: These are the disadvantages.which a firm faces due to expansion of its scale of production. They are:

• Lack of proper coordination among different departments of production process.
• Lack of control on inputs.
• Deterioration in communication between various departments.
• Lack of identification of errors committed.

(b) External Diseconomies: These are the disadvantages which the firms have to face due to expansion in the industry as whole. They are:

• Increased pressure on transportation – increase in cost of transport.
• Increase in pollution – rise in social cost.
• Shortage of capital-banks hesitate to finance.
• The factors of production becoming costly.
• Increase in business risk and marketing problems.

2nd PUC Economics Production and Cost Ten Marks Questions and Answers

Question 1.
Explain the meaning of various short-run costs with the help of a table and diagram.
The various short run costs are Total Cost, Total Fixed Cost, Total Variable Cost, Avenge Cost, Average Fixed Cost, Average Variable Cost, and Marginal Cost. The following table shows the various types of short run-costs:

Calcualtion of TFC, TVC, TC, AFC, AVC, AC and MC.

1. Total Fixed Cost (TFC):
It refers to the total money expenses incurred on alt the fixed factors in the short fun. TFC remains constant at all levels of output. Therefore the total fixed cost curve is a horizontal straight line parallel to ‘X’ axis above the origin which indicates that it is never zero.

2. Total Variable Cost (TVC):
It refers to the total money expenses incurred on the variable factor inputs in the short-run. Total variable cost is the direct cost of the output because it increases along with the output and remains zero when the output is zero. So, the TVC curves starts from the origin and rises sharply in the beginning, gradually in the middle and stretch again sharply in the end. The nature of this slope is in accordance with the law of variable proportion.

The Total Variable Cost is obtained as follows: TVC = TC – TFC

3. Total Cost (TC):
It is the aggregate money expenditure incurred by the firm on all the factors to produce a given quantity of output. TC varies in the same proportion as total variable cost because the total fixed cost is constant. The TC curve slope upwards from left to right, above the origin, indicating that, it includes total fixed cost and total variable cost.

4. Average Fixed Cost (AFC): ’
It is the fixed cost per unit of output. In other words, it is average expenses incurred on a single unit of output produced. AFC and output are in inverse relation i.e., AFC will be higher when the output level is less and as the output goes on increasing, AFC starts reducing. When represented in the diagram, AFC curve will have a negative slope which falls very stiffly in the beginning and later on becomes parallel to the X axis. This shows that it is never zero as TFC is never zero.

The Average Fixed Cost is obtained by dividing Total Fixed Cost by output.
AFC = TFC/output. .

5. Average Variable Cost (AVC):
It is a variable cost per unit of output. It can be calculated by dividing total variable cost by the total unite of output. When this cost is graphically represented, we get a ‘U’ shaped AVC, which shows that the cost will be less as the number of units produced increase, this is because as the number of variable inputs are added in a fixed plant the efficiency will increase and vice versa.
AVC = TVC/output or AVC = AC – AFC

6. Average Cost (AC):
It is the cost per unit of output produced. It is obtained by dividing total cost by the total output produced i.e, AC = TC/Q or it is also obtained by adding AFC and AVC. If the AC is graphical represented, we get a U shaped curve because of the operation of law of variable proportions. The short run AC curve is also called as ‘Plant Curves’ because it indicates the optimum utilization of a given plant (Industry) capacity.

7. Marginal Cost (MC):
It is an additional cost incurred to produce an additional output. In other words it is the net additions to the total cost when one more unit of output is produced.
MC=TCn – TCn-1
(Where TCn = Total cost of ‘n’ selected units of output and TCn-1 is total cost of the previous output)

Question 2.
Explain the law of variable proportions with the help of a table and diagram.
The Law of Variable Proportions (LVP) refers to input-output relationship, when the output is increased by varying the quantity of one input. This law operates in short period when all the factors of production cannot be increased or decreased simultaneously. The producer can enhance the output by increasing only one variable input by keeping other factors fixed. So, there will be change in proportion between Variable and Fixed Inputs. This is called as the Law of Variable proportions.

Assumptions of LVP:
The LVP operates under certain assumptions: They are:

• The technique of production remains same.
• There will be existence of Fixed inputs.
• The efficiency of variable inputs will be equal.
• There is possibility to change the proportion of inputs.
• The factor inputs are not close or perfect substitutes.

The law states that, an increase in variable inputs, in a given state of technology, cause output to increase, but after a point the extra output resulting from the same addition of extra inputs will become less and less.
The LVP can be illustrated with the help of a table:

In the above table, the producer (farmer) has 5 hectares of land in which he has spent Rs.25.000 for Agricultural machineries. When he increases labour input the TP, AP and MP increase in the beginning and later diminish. When the producer applies 3 units of labour the MP is highest at 30. Till here, the TP is in increasing returns. From 4th unit of labour, the MP and AP start decreasing. At 7th unit of labour the MP becomes zero indicating that the TP has reached optimum. When the producer uses 8th labour the MP becomes negative and TP starts falling.

Stages of LVP:
There are three stages of production as per LVP. (i) Increasing Returns (2) Diminishing Returns and (3) Negative Returns.

I Stage- Increasing Returns:
In this stage, TP increases at an increasing rate i.e., up to 3rd unit of labour, MP also rises and reaches maximum at this point and AP also goes on increasing.

Causes for Increasing Returns: The law of increasing returns operates because, in the beginning the quantity of fixed factors is abundant relative to the quantity of the variable factor. When the producer adds more units of variable input to the fixed factor of inputs, then the fixed factors are more intensively and effectively used. That means the efficiency of the fixed factors increase as additional units of the variable factors are added to it.

Another reason for increasing returns during first stage is that as more units of variable factors are employed, the efficiency of the variable factors itself increases. This is because with sufficient quantity of variabie factor, introduction of division of labour and specialization becomes possible which leads to increase in output.

II Stage – Diminishing Returns: .
In this stage, the TP continues to increase at a diminishing rate till it reaches 95 tons. Here, both AP and MP fall but they are positive. At the end of this stage, the MP becomes zero. This stage is called diminishing returns as both AP and MP start decreasing with the increase in inputs.

Causes for diminishing returns: When the producer increases the variable inputs even after the point where the variable input is sufficient to ensure efficient utilisation of the fixed factor, then further increase in the Variable factor will cause MP and AP to decline. This is because the fixed factor becomes inadequate relative to the quantity of variable factor.

Another reason for diminishing returns is the imperfect substitutability of one factor for another. If there is perfect substitute of the scarce fixed factor is available, the second stage would have been made up by increasing the supply of its perfect substitute with the result that output could be expanded.

III Stage-Negative Returns:
During the 3rd stage, the TP and AP will be falling and MP is negative. It is called negative returns as MP is negative.

Causes for negative returns: When the producer increases labour input beyond 6 units, the TP declines and MP becomes negative. This is due to the fact that the quantity of variable factor becomes too excessive in relation to the fixed factor so that they get in each other’s ways which result in decline in TP. In such situation, the producer has to reduce variable inputs to reduce the pressure on fixed factor.

Stage of operation-Production: Now the major question is which stage a rational producer will seek to produce? A rational producer will never produce in 3rd stage where MP is negative. The producer will also do not produce in first stage where the MP is increasing which is beneficial. If the producer selects to produce at first’stage, he will not be making best use of the fixed factor and he will not be utilizing fully the opportunities of increasing production by increasing quantity of the variable factor whose AP continues to rise throughout the first stage.

Thus, a rational producer will never produce in stage I and III. These stages are economic , non-sense. Hence it selects the II stage to produce.

The LVP can be represented in the following diagram:

In the above diagram, factor input labour is measures in OX axis and TP, AP and MP are measures on OY axis. In the first stage, the producer is producing RS of output with OS level of variable input. During this stage, TP, AP and MP are increasing.

When the producer increases input labour from OS to OU, the TP reaches maximum at TU in the second stage. Here TP curve is increasing but MP and AP curves are decreasing and MP reaches zero at point U. In the third stage, the TP, AP and MP are filling and MP becomes negative. Here, the TP falls from T and AP remains positive though it is falling.

Question 3.
Explain the meaning of laws of returns to scale with the help of arable and diagram.
We know that, in the long run all factor inputs are variable. The returns to scale explain the relationship between input and output in the long period. They study about the changes in output as a consequence of changes in all the inputs. This can be represented as follows:
Q = f(X1, X2,…….)

Stages of Returns to Scale: Returns to scale may be (1) Increasing Returns to Scale, (2) Constant Returns to Scale (3) Diminishing Returns to Scale.

These returns to scale can be seen in Total Product which, is the result of changes in all inputs.
1. Increasing Returns to Scale: Here, the output increases in a greater proportion than the increase in inputs. When a firm expands, increasing returns to scale are obtained in the beginning. For example, if there is 20% increase in inputs, the output increases by 30%. The increasing returns to scale also is a result of indivisibility of factors. Some factors are available in large and can be utilized with utmost efficiency at a large output.

2. Constant Returns to Scale: The constant returns to scale exists when the output increases in same proportion with the increase in inputs. For example, if a producer increase inputs by 25%, the Total product increases by 25%. Here the Total Product increases at constant rate. It has been found that an individual firm passes through a long phase of constant returns to scale in its lifetime.

3. Diminishing Returns to Scale: Also known as decreasing returns to scale operate when output increase in a smaller proportion with an increase in all inputs. For example, if a producer increases all inputs by 20%, the Total product increase in 15%. Diminishing returns to scale eventually occur because of increasing difficulties of management, coordination and control. When the firm has expanded to a very large size it is difficult to manage it with same efficiency as earlier. So, the diminishing returns to scale exist.

The returns to scale can be illustrated with the help of the table given below:

 Factor inputs (L+C) Total Product Marginal Product Returns to Scale 1+2 2+4 3+6 10 30 60 10 20 30 Increasing Returns to Scale 4+8 5+10 6+12 100 140 180 40 40 40 Constant Returns to Scale 7+4 8+16 9+8 210 230 240 30 20 10 Decreasing Returns to Scale

In the above table, we can-notice that the Total product is increasing at increasing rate (MP is increasing by 10, 20, 30, 40) with the increase in both the inputs Labour and Capital (L+C). If the producer increases the inputs any further, TP increases at constant rate (MP is constant at 40). Later, the TP increases at diminishing rate causing decreasing returns to scale (MP starts falling from 40, 30, 20, 10).

The laws of returns to scale can be graphically explained with the help of the following diagram:

In the above diagram, inputs are measured along the ‘X’ axis, Marginal Product is measured along ‘ Y’ axis. From point P to Q, it is increasing returns, from Q to R, it is constant returns and from R to S it is decreasing returns to scale.

Karnataka 2nd PUC Accountancy Question Bank Chapter 5 Accounting Ratios

2nd PUC Accountancy Accounting Ratios NCERT Textbook Questions and Answers

Percentage off calculator tool calculates percent off , increase and decrease with percentage discount formula.

Question 1.
What do you mean by Ratio Analysis?
Ratio Analysis is a technique of financial analysis. It describes the relationship between various items of Balance Sheet and Income Statements. It helps us in ascertaining profitability, operational efficiency, solvency, etc. of a firm. It may be expressed as a fraction, proportion, percentage and in times. It enables budgetary controls by assessing qualitative relationship among different financial variables.

Ratio Analysis provides vital information to various accounting users regarding the financial position and viability and performance of a firm. It also lays down the basic framework for decision making and policy designing by management.

Question 2.
What are the various types of ratios?
Accounting ratios are classified in the following two ways.
1. Traditional Classification: This classification is based on the financial statements, i.e. profit and Loss Account and Balance Sheet. The Traditional Classification further bifurcates accounting ratios as:
(a) Income Statement Ratios: These are those ratios whose all the elements belong only to the Trading and Profit and Loss Account, like Gross Profit Ratio, etc.
(b) Balance Sheet Ratios: These are those ratios whose all the elements belong only to the Balance Sheet, like Current Ratio, Debt Equity Ratio, etc,
(c) Composite Ratios: These are those ratios whose elements belong both to the Trading and Profit and Loss Account as well as to the Balance Sheet, like Debtors Turnover Ratio, etc.

2. Functional Classification: This classification reflects the functional need and the purpose of calculating ratio. The basic rationale to compute ratio is to ascertain liquidity, solvency, financial performance and profitability of a business. Consequently, the Functional Classification classifies various accounting ratios as:
(a) Liquidity Ratio: These ratios are calculated to determine short term solvency.
(b) Solvency Ratio: These ratios are calculated to determine long term solvency.
(c) Activity Ratio: These ratios are calculated for measuring the operational efficiency and efficacy of the operations. These ratios relate to sales or cost of goods sold.
(d) Profitability Ratio: These ratios are calculated to assess the financial performance and the financial viability of the business.

Question 3.
What relationships will be established to study?
(a) Inventory Turnover
(b) color Turnover
(c) Payables Turnover
(d) king Capital Turnover
(a) Inventory Turnover Ratio: This ratio is cc puted to determine the efficiency with which the stock is used. This ratio is b; scd on the relationship between cost of goods sold and average stock kept during the year

Cost of goods sold = Opening Stock + Purchases + Direct expenses – Closing Stock
Or cos to goods sold = Net sales – Gross Profit

(b) Debtors Turnover Ratio: This ratio is computed to determine the rate at which the amount is collected from the debtors. It establishes the relationship between net credit sales and average accounts receivables,

Net Credit Sales = Total Sales – Cash Sales
Average Account Receivables =

(c) Payable Turnover Ratio: This ratio is known as Creditors Turnover Ratio.’ It is computed to determine the rate at which the amount is paid to the creditors. It establishes the relationship between net credit purchases and average accounts payables.

Net Credit purchases = Total Purchases – Cash Purchases
Average Account Payable

(d) Working Capital Turnover Ratio: This ratio is computed to determine how efficiently the working capital is utilised in making sales. It establishes the relationship between net sales and working capital.
Working Capital Turnover Ratio =
Net Sales = total Sales – Sales Return
Working Capital = Current Assets – Current Liabilities.

Question 4.
Why would the inventory turnover ratio be more important when analysing a grocery store than an insurance company?
Grocery store is a trading concern and involved in business of buying and selling of grocery. It keeps stock of various groceries to meet the requirement of the customers and it should calculate the inventory turnover ratio. Hence, this ratio is more important for a grocery store then it is for an insurance company as the latter does not need to maintain any stock of goods sold. The insurance company is engaged in delivering service that is intangible and, thus, cannot be stored.

Question 5.
The liquidity of a business firm is measured by its ability to satisfy its long- term obligations as they become due? Comment.
The liquidity of a business firm is measured by its ability to pay its long term obligations, Die long term obligations include payments of principal amount on the due date and payments of interests on the regular basis. Long term solvency of any business can be calculated on the basis of the following ratios:

Debt-Equity Ratio: It depicts the relationship between the borrowed fund and owner’s funds. The lower the debt-equity ratio higher will be the degree of security to the lenders. A low debt-equity ratio implies that the company can easily meet its’long term obligations.

Total Assets to Debt Ratio: It shows the relationship between the total assets and the long term loans A high Total Assets to Debt Ratio implies that more assets are financed by the owner’s fund and the company can easily meet its long-term obligations.

Interest Coverage Ratio: This ratio depicts the relationship between amount of profit utilise for paying interest and amount of interest payable. A high Interest Coverage Ratio implies that the company can easily meet all its interest obligations out of its profit.

Proprietary Ratio: It shows the relationship between the Shareholders Fund and the Total Assets. This ratio reveals the financial position of a business. The higher the ratio the higher will be the degree of safety for.the creditors. It is calculated as:

Question 6.
The average age of inventory is viewed as the average length of time inventory, is held by the firm or as the average number of day’s sales in inventory. Explain.
Inventory Turnover Ratio: This ratio is computed to determine the efficiency with which the-stock is used. This ratio is based on the relationship between cost of goods sold and rage stock kept during the year. It shows the rate with which the stock is turned into sales Lite number of times the stock in turned into sales during the year. In other words, this ratio reveals the average length of time for which the inventory is held by the firm.

Cost of Goods Sold = Opening Stock + Purchases + Direct Expenses – Closing Stock
or, Cost of goods sold = Net Sales – Gross Profit

Question 1.
Who are the users of financial ratio analysis? Explain the significance of ratio analysis to them?
The users of financial ratio analysis are as follows:
1. Investors
2. Management
3. Short term Creditors
4. Long term Creditors.
The following points signify the importance of ratio analysis for these users.

1. Investors: The main concern for the investors is the security of the funds invested by them in the business and returns on their investments. The security of the funds is directly. related to the profitability and operational efficiency of the business. Consequently, they are interested in knowing Earnings per Share, Return on Investment and Return on Equity.

2. Management: They uses ratio analysis to determine how effectively the assets are being used. They are interested in future growth and prospects. They design various policy measures and draff future plAnswer: Consequently, they are interested in Activity Ratios and Profitability Ratios like, Net Profit Ratio, Debtors Tumover Ratio, Fixed Assets Tumover Ratios, etc.

3. Short-term Creditors: Short-term creditors are interested in timely payment of their debts in short run. Consequently, they are interested in Liquidity Ratios like, Current Ratio, Quick Ratios etc. These ratios reveal the current financial position of the business.

4. Long-term Creditors: Long-term creditors provide funds for more than one year, so they are interested in long term solvency of the firm and in assessing the ability of the firm to pay timely interests. Consequently, they are interested in calculating Solvency Ratios like,. Debt-Equity Ratio, Proprietary Ratio, Total Assets to Debt Ratio, Interest Coverage Ratio, etc.

Question 2.
What are liquidity ratios? Discuss the importance of current and liquid ratio.
Liquidity ratios are calculated to determine the short-term solvency of a business, i.e. the ability of the business to pay back its current dues. Liquidity means easy conversion of assets into cash without any significant loss and delay. Short-term creditors are interested in ascertaining liquidity ratios for timely payment of their debts. Liquidity ratio includes:

Current Ratio: It explains the relationship between current assets and current liabilities. It is calculated as:

Liquid Ratio or Quick Ratio: It explains the relationship between liquid assets and current liabilities. It indicates whether a firm has sufficient funds to pay its current liabilities immediately. It is calculated as:

Liquids Assets = Current Assets – Stock – Prepaid Expenses

Question 3.
How would you study the solvency position of the firm?
Solvency position of a firm is studied with the help of the Solvency Ratios. Solvency ratios are the measures of the long-term financial position of the firm in terms of its ability to pay its long-term liabilities. In other words, the solvency of the firm is measured by its ability to pay. its long term obligation on the due date. Long term solvency of any business can be calculated on the basis of the following ratios:

Debt-Equity Ratio: It depicts the relationship between the borrowed fund and owner’s funds. The lower the debt-equity ratio higher will be the degree of security to the lenders. A low debt-equity ratio implies that the company can easily meet its long term obligations. Equity or the Shareholders Fund includes.
Preference Share Capital, Equity Share Capital, Capital Reserve, Securities
Premium, General Reserve less Accumulated Loss and Fictitious Assets

Total Assets to Debt Ratio: It shows the relationship between the total assets and the long term loans A high Total Assets to Debt Ratio implies that more assets are financed by the owner’s fund and the company can easily meet its long-term obligations. Total Assets includes all fixed and current assets except fictitious assets like, Preliminary Expenses, Underwriting Commission, etc. Debt includes all long-term loans that are to be repaid after one year. It includes debentures, mortgage loans, bank loans, loans from other financial institutions, etc.

Interest Coverage Ratio: This ratio depicts the relationship between amount of profit utilise for paying interest and amount of interest payable. A high Interest Coverage Ratio implies that the company can easily meet all its interest obligations out of it’s profit.

Proprietary Ratio: It shows the relationship between the Shareholders Fund and the Total Assets. This ratio reveals the financial position of a business. The higher the ratio the higher will be the degree of safety for the creditors, It is calculated as:
Proprietary Ratio

Question 4.
What are important profitability ratios? How are they worked out?
Profitability ratios are calculated on the basis of profit earned by a business. This ratio gives a percentage measure to assess the financial viability, profitability and operational efficiency of the business. The various important Profitability Ratios are as follows:
Gross Profit Ratio: It shows the relationship between Gross Profit and Net Sales. It depicts the trading efficiency of a business. A higher Gross Profit Ratio implies a better position of a business, whereas a low Gross Profit Ratio implies an inefficient unfavourable sales policy.

Gross Profit = Net Sales – Cost of Goods Sold
Net sales = Total Sales – Sales Return
Cost of Goods Sold = Opening Stock + Purchases + Direct Expenses — Closing Stock

Operating Ratio: It shows the relationship between Cost of Operation and Net Sales. This ratio depicts the operational efficiency of a business. A low Operating Ratio implies higher operational efficiency of the business. A low Operating Ratio is considered better for the business as it enables the business to be left with a greater amount after covering its operation costs to pay for interests and dividends.

Operating Cost = Cost of Goods Sold + Operating Expenses
Cost of Goods Sold = Sales – Gross Profit

Operating Profit Ratio: It shows the relationship between the Operating Profit and Net Sales. It helps in assessing the operational efficiency and the performance of the business.

Operating Profit Ratio = 100 – Operating Ratio
Operating Profit = Sales – Operation cost

Net Profit Ratio: It shows the relationship between net profit and sales. Higher ratio is better for firm. It depicts the overall efficiency of a business and acts as an important tool to the investors for analysing and measuring the viability and performance of the business.

Net Sales = Total Sales – Sales Return

Return on Investment or Capital Employed: It shows the relationship between the profit earned and the capital employed to earn that profit. It is calculated as:

Capital Employed = Fixed Assets + Current Assets- Current Liabilities
Or, Capital Employed = Share Capital + Reserve and Surplus + Long-term Funds-Fictitious Assets

Earning per Shares: It shows the relationship between the amount of profit available to distribute as dividend among the equity shareholders and number of equity shares

Profit available for equity shareholers = Net Profit after tax

Dividend payout Ratio: It shows the relationship between the dividend per share and earnings per share. This ratio depicts the amount of earnings that is distributed in the form of dividend among the shareholders. A high Dividend Payout Ratio implies a better position and goodwill of the business for the shareholders.

Price Earnings Ratio: It shows the relationship between the market price of a share and the earnings per share. This ratio is the most common tool that is used in the stock markets. This ratio depicts the degree of reliance and trust that the shareholders have on the business.

Question 5.
Financial ratio analysis is conducted by four groups of analysts: managers, equity investors, long-term creditors, and short-term creditors. What is the primary emphasis of each of these groups in evaluating ratios?
Financial ratio analysis is conducted by four groups of analysts: managers, equity investors, long term creditors and short term creditors. The primary emphasis of each of these groups in evaluating ratios is:
1. Management: They use ratio analysis to determine how effectively the assets are being used. They are interested in future growth and, prospects. They design various policy measures and draft future plans Consequently, they are interested in Activity Ratios and Profitability Ratios like Net Profit Ratio, Debtors Turnover Ratio, Fixed Assets Turnover Ratios, etc..

2. Equity Investors: The main concern for the investors is the security of the funds invested by them in the business and returns on their investments. The security of the funds is directly related to the profitability and operational efficiency of the business. Consequently, they are interested in knowing Earnings per Share, Return on Investment and Return on Equity.

3. Long-term Creditors: Long-term creditors provide funds for more than one year, so they are interested in long term solvency of the firm and in assessing the ability of the firm to pay timely interests. Consequently, they are interested in calculating Solvency Ratios like, Debt-Equity Ratio, Proprietary Ratio, Total Assets to Debt Ratio, Interest Coverage Ratio, etc.

4. Short-term Creditors: Short-term creditors are interested in timely payment of their debts in short run. Consequently, they are interested in Liquidity Ratios like, Current Ratio, Quick Ratios etc. These ratios reveal the current financial position of the business.

Question 6.
The current ratio provides a better measure of overall liquidity only when a firm’s inventory cannot easily be converted into cash. If inventory is liquid, the quick ratio is a preferred measure of overall liquidity. Explain.
Current Ratio: It explains the relationship between current assets and current liabilities. It is calculated as:

Currents Assets are those assets that are easily converted into cash within a short period of time like cash in hand, cash at bank, marketable securities, debtors, stock, bills receivables, prepaid expenses, etc.

Current Liabilities are those liabilities that are to be repaid within a year like bank overdraft, bills payables, Short-term creditors, provision for tax, outstanding expenses etc:

Liquid Ratio: It explains the relationship between liquid assets and current liabilities. It indicates whether a firm has sufficient funds to pay its current liabilities immediately. It is calculated as:

Liquid Assets = Current Assets – Stock – Prepaid Expenses

Generally, Current Ratio is preferable for such type of business where the stock or the inventories cannot easily be converted into cash like heavy machinery manufacturing companies, locomotive companies, etc. This is because, the heavy stocks like machinery, Heavy tools etc. cannot be easily sold off. But on the other hand, the businesses where the stock can be easily realised or sold off regard Liquid Ratio to be more suitable measure to reveal their liquidity position. For example, the inventories of a service sector company are very liquid as there is no stock kept for sale, so they prefer Liquid Ratio as a measure of overall liquidity.

Moreover, sometimes companies prefer to resort to Liquid Ratio instead of Current Ratio, if the prices of the stock held are prone to fluctuate. This is because if the prices of the inventories fluctuate more, then this may affect their liquidity position of the business and may reduce (or overcast) the Current Ratio. Consequently, they prefer Liquid Ratio as it excludes inventories and stocks.

Thirdly, if the stock forms the major portion of a company’s current assets, then they would prefer Current Ratio and not Liquid Ratio. This is because their current assets mostly consist of stock. The Liquid Ratio of such company will be very low as liquid assets exclude stock. This will reduce their Liquid Ratio and may create a bad image’for the creditors. In such a case, Current Ratio provides better measure of overall-liquidity.

2nd PUC Accounting Ratios Numerical Questions

Question 1.
Following is the Balance Sheet of Raj Oil Mins Limited as at March 31,2015. Calculate current ratio.

Current assets = Stock + Debtors + Cash at bank
= 55,800 + 28,800 + 59,400 = 1,44,000
= 72,000
Current Ratio = $$\frac{1,44,000}{72,000}=\frac{2}{1}$$ = 2:1

Question 2.
Following is the Balance Sheet of Title Machine Ltd. as at March 31,2015.

Calculate Current Ratio and Liquid Ratio.

Current Assets = Inventories + Trade Receivables + Cash + Short term Loans and Advances
= 12,00,000+ 9,00,000+ 2,28,000+ 60,000 = ₹ 24,00,000
Current Liabilities = Trade Payables + Short-term Borrowing + Short-term Provisions
= 23,40,000 + 6,00,000 = 60,000 = ₹ 30,00,000

2. Quick Ratio

Quick Assets = Trade Receivables + Cash + Short term Loans and Advances,
= 9,00,000 + 2,28,000 + 72,000 = ₹ 12,00,000

Question 3.
Current Ratio is 3.5 : 1. Working Capital is ₹ 90,000. Calculate the amount of Current Assets and Current Liabilities.

or, Current Assets = 3.5 Current Liabilities (1)
Working Capital = Current Assets – Current
Liabilities Working Capital = 90,000
or, Current Assets – Current Liabi lities = 90,000
or, 3.5 = Current Liabilities – Current Liabilities = 90,000 (from I)
or, 2.5 Current Liabilities = $$\frac { 90,000 }{ 2.5 }$$ = 36,000
or Current Assets = 3.5 Current Liabilities
= 3.5 × 36,000= 1,26,000

Question 4.
Shine Limited has current 1 and quick ratio 3 : 1; if the inventor is 36,000, calculate Current Liabilities, and Current Assets.

Quick Assets = Current Assets – Stock
= Current Assets – 36,000
or, 4.5 Current Liabilities – 3 Current Liabilities = 36,000
or, 1.5 Current Liabilities = 36,000 or, Current Liabilities = 24,000
Current Assets = 4.5 current Liabilities
or, Current Assets = 4.5 × 24,000 = 1,08,000

Question 5.
Current Liabilities of a company are ₹ 75,000. If current ratio is 4 : 1 and Liquid Ratio is 1: 1, calculate value of Current Assets, Liquid Assets and Inventory.

or, 4 × 75,000 = Current Assets
or, Current Assets = 3,00,000

Current liabilities
Liquid Assets = 75,000
Stock = Current Assets -Liquid Assets = 3,00,000 – 75,000
= 2,25,000

Question 6.
Handa Ltd. has inventory of ₹ 20,000. Total liquid assets are ₹ 1,00,000 and quick ratio is 2: 1. Calculate current ratio.

Or, Current liabilities = $$\frac{1,00,000}{2}$$ = 50,000
Current Assets = Liquid Assets + inventory
= 1,00,000 + 20,000 = 1,20,000

Question 7.
Calculate debt-equity ratio from the following information:
Total Assets ₹ 15,00,000
Current Liabilities ₹ 6,00,000
Total Debts ₹ 12,00,000

Equity = Total Assets – Total Debts
= 15,00,000 – 12,00,000 = 3,00,000

Long Term Debts = Total  Debts – Currrent Liabilities

Question 8.
Calculate Current Ratio if:
Inventory is ₹ 6,00,000; Liquid Assets ₹ 24,00,000; Quick Ratio 2 : 1.

Current liabilities = $$\frac { 24,00,000 }{ 2 }$$ = 12,00,000
Current Assets = Liquid Asset + Inventory = 24,00,000 + 6,00,000 = 30,00,000

Question 9.
Compute Inventory Turn over Ratio from the following information:
Net Revenue from Operations ₹ 2,00,000
Gross Profit ₹ 50,000 .
Inventory at the end ₹ 60,000
Excess of inventory at the end over
inventory in the beginning ₹ 20000

Cost of Goods sold = Net Sales – Gross Profit
= 2,00,000 – 50,000= 1,50,000
Opening Stock = Closing Stock – 20,000
= 60,000 – 20,000 = 40,000

Average Inventory = $$\frac{40,000+60,000}{2}=\frac{1,00,000}{2}$$ = 50,000
Stock turnover ratio = $$\frac{1,50,000}{50,000}=\frac{3}{1}$$ = 3 times

Question 10.
Calculate following ratios from the following information:
(i) Current ratio
(ii) Liquid ratio
(iii) Operating Ratio
(iv) Gross profit ratio
Current Assets . ₹ 7 35,000
Current Liabilities ₹ 17,500
Inventory ₹ 15,000
Operating Expenses ₹ 20,000
Revenue from Operations ₹ 60,000
Cost of Revenue from operation ₹ 30,000

Liquid assets = current assets – stock
=35,000- 15,000 = 20,000
Acid test ratio = $$\frac{20,000}{17,500}=\frac{1.413}{1}$$ = 1.143:1

Question 11.
From the following information calculate:
1. Gross Profit Ratio
2. inventory Turnover Ratio
3. Current Ratio
4. Liquid Ratio
5. Net Profit Ratio
6. Working Capital Ratio:
Revenue from Operations ₹15,20,000
Net Profit ₹ 3,60,000
Cost of Revenue from Operations ₹ 19,20,000
Long-term Debts ₹ 9,00,000
Average 7 aventory ₹ 8,00,000
Current Assets ₹ 7,60,000
Fixed Assets ₹ 14,40,000
Current Liabilities ₹ 6,00,000
Net Profit before Interest and Tax ₹ 8,00,000
1.

Gross Profit = Revenue from operation – Cost of Sales
= 25,20,000- 19,20,000 = 6,00,000
Gross Profit ratio = $$\frac{6,00,000}{25,20,000} \times 100$$ = 23.81

2.

$$=\frac{19,20,000}{8,00,000}=\frac{2.4}{1}=2.4: 1$$

3.

Current Asset = Liquid Assets + Inventory
= 7,60, 000 + 8,00,000 = 15,60,000
Current ratio = $$\frac{15,60,000}{6,00,000}=\frac{2.6}{1}=2.6: 1$$

4.

5.

6.

Working capital = Current Assets – Current Liabilities
= 15,60,000 – 6,00,000 = 9,60,000
Working Capital Ratio $$=\frac{25,20,000}{9,60,000}$$ = 2.625 times .

Question 12.
Compute Gross Profit Ratio, Working Capital Turnover Ratio, Debt Equity Ratio and Proprietary Ratio from the following information:
Paid-up Share Capital ₹ 5,00,000
Current Assets ₹ 4,00,000
Revenue from Operations ₹ 10,00,000
13% Debentures ₹ 2,00,000
Current Liabilities ₹ 2,80,000
Cost of Revenue from Operations ₹ 6,00,000

Gross Profit = Net revenue from operations – Cost of Goods Sold
= 10,00,000 – 6,00,000 =4,00,000
Gross profit ratio = $$\frac{4,00,000}{10,00,000} \times 100$$ = 40%
Working Capital = Current Assets – Current Liabilities
= 4,00,000 – 2,80,000 = 1,20,000
Working Capital Ratio = $$\frac { 10,00,000 }{ 1,20,000 }$$ = 8.33 times

Total Assets = Paid up Capital + Debentures + Current Liabilities
(∵ Total Liabilities = Total Assets)
= 5,00,000 + 2,00,000 + 2,80,000 =9,80,000
Proprietary ratio = $$\frac { 5,00,000 }{ 9,80,000 }$$ = 25:49 = 0.51:1

Question 13.
Calculate Inventory Turnover Ratio if:
Inventory in the beginning is ₹ 76,250, Inventory at the end is 98,500, Gross Revenue from Operations is ₹ 5,20,000, Sales Return is ₹ 20,000 Purchases is ₹ 3,22,250.
Ans:
Gross Profit Ratio = $$\frac { 4,00,000 }{ 10,00,000 }$$ × 100 = 40%
Cost of Goods Sold = Opening Inventory + Purchases – Closing Inventory
= 76,250 + 3,22,250 – 98,500 = 3,00,000

Stock Turunover Ratio = $$\frac { 3,00,000 }{ 87,375 }$$ = 3,43 times

Question 14.
Calculate inventory Turnover Ratio from the data given below:
Inventory in the beginning of the year ₹ 10,000
Stock at the end of the year ₹ 5,000
Carriage ₹ 2,500
Revenue from Operations ₹ 50,0130
Purchases ₹ 25,000

Cost of Goods Sold = Opening Stock + Purchases + Carriage – Closing Stock
= 10,000 + 25,000 + 2,500-5,000 = 32,500

Stock turnover ratio = $$\frac{32,500}{7,500}$$ = 4.33 times

Question 15.
A trading firm’s average inventory is ₹ 20,000 (cost). If the inventory turnover ratio is 8 times and the firm sells goods at a profit f 20% on sales, ascertain the profit of the firm.

or, Cost of Goods Sold = 20,000 × 8
or, Cost of Goods Sold = 1,60,000
Let Sale Price be ₹ 100
Then Profit is ₹ 20
Hence, the Cost of Revenue from Operations = ₹ 100
₹ 20 = ₹ 80 If the Cost of Revenue from Operations is ₹ 80, then Revenue from operations = 100
If the Cost of Revenue from Operations is ₹ 1, then Revenue from operations = $$\frac { 100 }{ 80 }$$
If the Cost ofGoods Sold is 1,60,000 then Sales = $$\frac { 100 }{ 80 }$$ × 1,60,000 = 2,00,000
Profit = Revenue from Operations
=2,00,000 – 1,60,000 = ₹ 40,000

Question 16.
You are able to collect the following information about a company for two years:

Calculate Inventory Turnover Ratio and Trade Receivables Turnover Ratio

or, Cost of Revenue from Operations = Revenue from operations – Gross Profit
or, Gross Profit = 25% of Sales
= 25% of 24,00,000 =6,00,000
or, Cost of Goods sold = 24,00,000 – 6,00,000 = 18,00,000

Debtors Turnover Ratio = $$\frac { 24,00,000 }{ 5,30,000 }$$ = 4,53 times
Note: It has been assumed that all Revenue from operations are credit Revenue from operations

Question 17.
From the following Balance Sheet and other information, calculate following ratios:
1. Debt-Equity Ratio
2. Working Capital Turnover Ratio

Additional Information: Revenue from Operations ₹ 18,00,000 (Debt-Equity Ratio 0.63 : 1; Working Capital Turnover Ratio 1.39 times; Trade Receivables Turnover Ratio 2 times)
1. Debt – Equity Ratio

Debt = Long Term Borrowings = ₹ 12,00,0000
Equity = share Capital + Reserve and Surplus
= 10,00,000 + 9,00,000 = ₹ 19,00,000

2. Working Capital Turnover Ratio
Working Capital Turnover Ratio

Revenue from Operations = ₹ 18,00,000
Working capital = Current Assets – Current Liabilities
= 18,00,000 – 5,00,000 = ₹ 13,00,000

Net credit sales = ₹ 18,00,000
Avereagre Trade Receivables = ₹ 9,00,000
Notes:
1. Revenue from Operations are assumed to be revenue generated from credit sales.
2. The amount of trade receivables given in the Balance Sheet is assumed to be Average Trade Receivables.

Question 18.
From the following information, calculate the following ratios:
1. Liquid Ratio
2. Inventory turnover ratios
3. Return on investment

1.

Quick Assets = Cash + Debtors
= 40,000+ 1,00,000 = 1,40,000
Current Liabilities = Creditors + Outstanding Expenses
= 1,90,000 + 70,000 = 2,60,000
Quick Ratio = $$\frac{1,40,000}{2,60,000}$$ =7:13 = 0.54:1

2.

Cost of Revenue from Operations = Revenue from Operations – Gross profit
= 4,00,000- 1,94,000 = 2,06,000

$$=\frac{50,000+60,000}{2}=55,000$$
Inventory Turnover Ratio = $$\frac{2,06,000}{55,000}$$ = 3.74 times

Capital Employed = Equity share capital + Profit and Loss
= 2,00,000 + 1,40,000 = 3,40,000
Return on Investment = $$\frac{1,40,000}{3,40,000}$$ × 100 – 41.17%

Question 19.
From the following, calculate
(a) Debt-Equity Ratio
(b) Total Assets to Debt Ratio
(c) Proprietary Ratio.

Equity / Share holders Funds = Equity Share Capital + Preference Share Capital + General Reserve +Accumulated Profit – Preliminary Expenses Written off
= 75,000 + 25,000 + 50,000 + 30,000 – 5,000=1,75,000

Question 20.
Cost of Revenue from Operations is ₹ 1,50,000. Operating expenses are ₹ 60,000. Revenue front Operations is ₹ 2,50,000. Calculate Operating Ratio.

Question 21.
Calculate the following ratio on the basis of following information:
1. Gross Profit Ratio
2. Current Ratio
3. Acid Test Ratio
4. Inventory Turnover Ratio
5. Fixed Assets Turnover Ratio

1.

2.

Current Assets = Inventory + Trade Receivables + Cash and Cash Equivalents
= 15,000 + 27,500 + 17,500 = 60,000
Currebt Ratio = $$\frac{60,000}{40,000}=1.5: 1$$

3.

Liquid Assets = Current Assets – Inventory
= 60,000 – 15,000 = 45,000
Acid test ratio = $$\frac{45,000}{40,000}=1.125: 1$$

Question 22.
From the following information calculate Gross Profit Ratio, Inventory Ratio and Trade Receivable Turnover Ratio.
Revenue from Operations ₹ 2,00,000
Cost Of Revenue from Operations ₹ 2,40,000
Inventory at the end ₹ 62,000
Gross Profit ₹ 60,000
Inventory in the beginning ₹ 58,000

Gross Profit = Net Revenue from Operation – Cost of Goods Sold
= 3,00,000 – 2,40,000 = 60,000
Gross Profit Ratio $$=\frac{60,000}{3,00,000}$$ × 100 = 20%

$$=\frac{58,000+62,000}{2}=\frac{1,20,000}{2}=60,000$$
Stock. Turnover Ratio = $$\frac{2,40,000}{60,000}$$ = 4 times

Note: In the solution, the Trade receivables are assumed as the average Trade receivables

Karnataka 2nd PUC Statistics Question Bank Chapter 1 Vital Statistics

2nd PUC Statistics Vital Statistics One and Two Marks Questions and Answers

Question 1.
Define vital statistics.
Vital statistics is the science, which deals with the analysis and interpretation of numerical facts regarding vital events occurring in a human population

Question 2.
What are vital events?
Vital events are the events, which are occurring, in human life such as births, deaths, sickness, marriages, divorce, migration etc.

Question 3.
Mention any two uses of Vital Statistics.
Vital Statistics is used,

1. to study the Demographic structure & trend in the population
2. use in public administration. OR
3. use to operating agencies
4. to researchers

Question 4.
What are the sources of vital statistics?
Registration method and Census method

Question 5.
Define C.B.R, G.F.R, A.S.F.R, C.D.R, A.S.D.R, S.D.R, M.M.R, I.M.R, N.M.R, G.R.R, and N.R.R.
CBR is defined as the average number of live births occurring in a population of 1000 in a year.

• GFR is defined as the average number of live births occurring to 1000 women of childbearingage in a year;
• ASFR is defined as the average number of live births occurring to 1000 women of specified age in a year.
• CDR is the average number of deaths occurring in the year per 1000 population.
• ASDR is the average number of deaths occurring in the year in the specified age group.
• SDR is defined as the weighted average of ASDR’s with respect to standard population
ie SDR = $$\frac{\Sigma \mathrm{PA}}{\Sigma \mathrm{P}}$$
• IMR is defined as the average number of deaths of Infants in a year per 1000 infant population.
• MMR is defined as the ‘the number of deaths of mothers due child birth occurring in a region’ in the year per 100,000 live births.
• NMR: Neo-natal mortality rate is defined as ‘the average number of neo-natal deaths 1000 live births in a year’.
• The gross reproduction rate (GRR) is the average number of daughters that would be born to a woman (or a group of women) if she survived at least to the age of 45 and conformed to the age-specific fertility rate of a given year.
• Neo-natal mortality rate is defined as ‘the average number of neo-natal deaths 1000 live births in a year’.
OR Write the formula of all the above.

Question 6.
What is Death Rate/Mortality Rate?
It is the number of deaths occurring in the population OR It is the rate of decrease of population due deaths occurring in the population per 1000 population in the year.

Question 7.
What is a Life table?
Life table is a tabular presentation of numerical data describing the mortality experience of a cohort.

Question 8.
What is cohort?
Cohort is a group of individuals who born at the same and experiences the same mortality conditions

Question 9.
Radix is the size of the cohort, and usually is 100,000 individuals

Question 10.
What is the Life expectancy/Expectation of life?
It is the expected number of years of life that a person of age ‘x’ can live there after.

Calculate the age of a person, place or anything else. This age calculator calculates age for a date of birth on any given date in years, months and days.

Question 11.
Mention any one use of Life table.
They are used in computation of actuarial of premium, bonus etc, of policies by Insurance Agencies. OR

• Life Tables are used in research activities in Biology, Medicine, Pharmacology, Demography, Psychology, Sociology etc.
• They are used to study population growth and forecast the size and sex distribution of the
Population. OR
• Life Tables give Mortality and Survival ratios at different ages.
• Life tables give the life expectancy at different age. OR
• These are useful in public administration, heath care, planning and population control

Question 12.
Define Total fertility rate.
If ASFR is calculated for the age group of 5 years, then,
TFR = 5 ΣQuinqennial ASFR

Question 13.
What are Quinquennial A.S.F.R’s?
If the A.S.F.R’s calculated with a width of 5 years are called Quinquennial ASFR’s.

Question 14.
Given E Quinqennial ASFR = 400, find TFR.
TFR = 5 ΣQuinqennial ASFR = 5 x 400 = 2000 . .

Question 15.
Explain briefly Registration method.
Registration method is the method of continuous, permanent and compulsory recording of vital events due to the legal importance occurring in the population as and when they happen. Vital statistics are obtained from the records of Zilla panchayath offices, Taluk panchayath offices, Hospitals etc, when births are registered the information regarding sex of a baby, age and religion of a mother, father are recorded.

Question 16.
Explain briefly the census method.
Census method is the method of complete enumeration of each and every unit of the population of the particular area under study, in India Decennial census [once in every ten years]are conducted, at the census, including all the vital events, an exhaustive information regarding economic and social status of the population are also collected.

Age Difference Calculator is a free online tool that displays the difference in age between two dates.

Question 17.
State any two differences between
(a) C.D.R & S.D.R.
(b) C.B.R. & G.F.R (Give any two comparisons between CDR AND STDR)
(a) CDR is a approximate measure of mortality-SDR is used for comparison of mortality
CDR does not consider the age composition of the population- SDR consider the age composition of the Population.
Differences between CDR and SDR:

 SL.No CDR SDR 1. It does not require age composition It require age composition 2. It cannot be used for comparison of mortality of different localities It be used for comparison of mortality of different localities 3. It needs no. of deaths and It needs deaths, population and population standard population

(b) CBR indicates the growth of population of due to births-GFR does not indicate the growth of population due to births, because it is based on only a part of the population CBR considers the population as a whole-GFR considers only women population of childbearing age.

Question 18.
Define Maternal Mortality Rate
MMR is defined as the ‘the number of deaths of mothers due child birth occurring in a region’ for every 100,000 births occurring in the year.

Question 19.
Which measure is used for comparing the ‘health conditions’ of two towns?
SDR’s

Question 20.
In a year, the CDR for a population of 3 lakhs is 8. Find the number of deaths.
Number of deaths occurring in the year
Ans

Question 21.
What is Birth Rate/Fertility Rate?
It is the number of live births occurring to women of child bearing age OR It is rate of increase of population due births occurring to women of child bearing age per 1000 population in the year

Question 22.
What is Longevity in Life table?
Longevity is the expected number of years that a newborn baby would live. OR “Life expectancy, of a new born baby is called Longevity”

Question 23.
Write down the components of a Life table
Components of Life table is:-

Question 24.
In a community, in a specific year, 3250 live births occurred. In the case of 35 of the above, the mother died due to childbirth. Compute M.M.R.[per 1000]

Question 25.
In a community, in a specific year, 4000 live births occurred. In the case of 50 of the above, the mother died due to child birth. Compute M.M.R.[per 1000].

Question 26.
The Quinquennial ASFRs for women of childbearing age of a community are 26 63, 65, 46, 24, 13, and 7. Compute TFR.
T.F.R = ΣQuinquennial ASFRs = 5 [26 + 63 + 65 + 46 + 24 + 13 + 7] = 1220

Question 27.
Calculate Maternal Mortality Rate [per 1000] from the following data.

Question 28.
In a year, the average population of town was 1, 50,000. The number of live births occurred in that year in the town was 6,000.Find Crude Birth Rate
Write CBR formula; CBR = $$\frac{6000}{150000}$$ x 1000 = 40

Question 29.
Find Pt given Po = 1,26,305; Births = 24,500; Deaths = 4,050; Immigrants = 8,065 and Emigrants=6000.
Pt = P0 + (B – D) + (I – E); = 1,48,820.

Question 30.
In a year, in a community there were 6500 live births. The number of infants died in the year was 350, of the infants deaths in 18 cases the new born babies died within one month. Find IMR and NMR.

Question 31.
The quinquennial age specific fertility rates for women of child bearing age group of a community are 25, 60, 70, 40, 20, 12 and 5. Compute TFR.
TFR = 5 ΣQuinquennial ASFRs = 5 x [25 + 60 + 70 + 40 + 20 + 12 + 5]
= 5 x 232 = 1160.

Question 32.
What is death rate?
It is the number of deaths occuring in the population in the given region of 1000 population.

Question 33.
Mention any two measures of Mortality.
Crude Death rate, Age specific death rate.

Question 34.
Mention any two measure sof Fertility.
Crude Birth rate, General Fertility, etc.

Question 35.
What is Motality ratio?
It is the ratio that a randomly selected person aged ‘x’ years does not survive till the age of (x + 1) years denoted by $$\mathrm{q}_{\mathrm{x}}=\frac{\mathrm{d}_{\mathrm{x}}}{l_{\mathrm{x}}}$$

Question 36.
What is survival ratio?
It is the ratio that a randomly selected person aged ‘x’ can survive till that age (x + 1) year denoted by Px = 1= qx.

Question 37.
What do you mean by Quinquennial ASFR’s?
If ASFR’s calculated for the age group of 5 years. It is called Quinquennial ASFR’s.

Question 38.
Write any two differences of CBR and ASFR.

• CBR is the average number of live birth occuring in the year per 1000 population.
• ASFR is the average number of live births occuring in the specified age group in the year per 1000 women in the specific age group.
• CBR, does not include the age and sex composition of the population.
• ASFR it includes the age and sex composition of the population.

Question 39.
Mention any two differences of CDR and ASDR.

• CDR is the number of deaths occuring in the year per 1000 population.
• ASDR in the number of deaths occuring in the specific age group in the year per 1000 population of the specific age group.
• CDR does not consider the age composition of the population.
• ASDR takes into consideration of the age composition of the population.

Question 40.
Explain briefly Registration method.
Registration method is the method of continous, permanent and compulsory recording of vital events due to the legal importance.

Question 41.
Explain briefly census method?
Census method is the complete enumeration of each and every unit of the population of the particular area under study.

Question 42.
What is total fertility rate?
It is the sum of annual ASFR’s for all age groups (15 – 49) years,
i.e., TFR = Σ annual ASFR’s.
If it is calculated for the age groups of 5 years called quinquennial ASFR’s.
Then, TFR = 5 Σ Quinquennial ASFR’s.

Question 43.
Give the formula for calculating Infant mortality rate.
Infant mortality rate (I.M.R)

Question 44.
Give the formula for calculating matenal mortality rate.

Question 45.
What is standardised death rate?
Standardised death rate is the weighted Arithmatic mean of deaths in the different age groups and the standard population in the age group
i.e; SDR = $$\frac{\Sigma \mathrm{PA}}{\Sigma \mathrm{P}}$$
where P – Standard Population ; A – ASDR’s

Question 46.
Give the formula obtaining the population in between two census.
Pt = Po (B – D) + (I – E) ; where Pt = Population after time ‘t’ after census year.
P0 = Population in the census year.
B, D, I and E – Births, deaths, immigrations and emigrants in the time period.

Question 47.
Calculate ASFR’s for the age groups (10 – 20) and (20 – 40) years.

ASFR = (10 – 20) = $$\frac{410}{15000}$$ x 1000 = 27.3
ASFR = (20 – 40) = $$\frac{650}{22000}$$ x 1000 =29.55

Question 48.
Compute general fertility rate from the data given below:

General Fertility rate;

Question 49.
Calculate ASDR’s for the age groups (0-5) and (40-60) years from the following data.

ASFR = (0 – 5) years = $$\frac{410}{22000}$$ x 1000 = 18.63
ASFR = (40 – 60) = $$\frac{150}{8000}$$ x 1000 = 18.75

Question 60.
If TFR of a certain locality is 2750 then find the average number of children born to Women.
Average number of children bom to Women = $$\frac{TFR}{1000}$$ = $$\frac{2750}{1000}$$ 2.75 = 3 (Approx)

Question 61.
The certain town, in a year 25000 births have occured. The number of infant deaths in the year was 1350. Among the live births in 150 cases, mother died due to child birth problems. Calculate infant motality rate and maternal mortality rate.
The imfant mortality rate:

Question 62.
In a town, in a year 2200 live births occurred and of these 430 died in the same year. Find IMR.

Question 63.
Calculate Infant mortality rate from the following data.

Question 64.
Calculate maternal mortality rate from the following data.

The maternal mortality rate is

Question 65.
In a town, 231440 births occured in an year and 7860 infants died in the same year. Find I.M.R.
Infant Mortality Rate is:

Question 66.
In an year, in a community there were 12750 live births occurred. 103 of these babies lost their mothers at the time of delivery. Find MMR.
The maternal mortality rate is:

Question 67.
In a given year, the CDR for a population of 1,50,000 is 12. Find the number of deaths.
CDR = 12 ; Population = 1,50,000

Question 68.
Calculate metarnal mortality rate (per 1000) from the following data.

Maternal Mortality Rate (M.M.R) is

Question 69.
In a year the C.D.R. for a population of 3 lakhs is 8. Find the number of deaths.
Crude Death Rate (C.D.R.)

Question 70.
In a community, in a specific year, 3250 live births occurred. In the case of 35 of the above, the mother died due to childbirth. Compute M.M.R. (per 1000).
Maternal Mortality Rate –

M.M.R = 10.769.

Question 71.
In a particular city out of 1800 live births in a year, 90 newborn babies died within 28 days. Calculate neonatal mortality rate.
Neo-natal mortality rate:

Question 72.
In a town, in a year 3120 live births occurred and of these 160 infants died in the same year. Of all the newborn babies in 15 cases died within one month. Compute I.M.R and N.M.R.

2nd PUC Statistics Vital Statistics Five Marks Questions and Answers

Question 1.
Explain Registration method and Census method of collecting Vital Statistics.
Registration method is the method of continuous, permanent and compulsory recording of vital events due to the Legal importance. When ever Vital events Occur in the population, are registered at the Registers of municipal offices, panchayat offices, Hospitals etc. When births are registered information of age of mother, caste, sex of a baby etc., are registered. Similarly when death occurred, information regarding sex , religion, marital status, age of death, cause of death etc., are registered.

Census method is the complete enumeration of each and every unit of the population of a particular area under study, at regular intervals. In India, once in every 10 years census is conducted. In this method information regarding birth, death, marriage, literacy etc., are collected.

Question 2.
In a year in a population of 1,00,000, there were 18S0 live births and 1680 deaths. Assuming the population is closed for migration. Calculate CBR and CDR.
P0 = 1,00,000, B= 1850, D= 1680
Pt = Population at the end of the year = P0 + (B – D)
= 1,00,000+ (1850 – 1680) = 1,00,170

Question 3.
The following data gives the age distribution and number of deaths in a population. Find ASDR’s.

ASDR. (Below 10 years) = $$\frac{215}{21000}$$ x 1000 = 10.24
ASDR (10-20) years = $$\frac{150}{16000}$$ x 1000 = 9.375
ASDR (20-30) = $$\frac{75}{15000}$$ x 1000 = 5
ASDR (30-40) = $$\frac{15}{12500}$$ x 1000 = 1.2
ASDR(40-50) = $$\frac{22}{4000}$$ x 1000 =5.5
ASDR (50 and above) =$$\frac{38}{1300}$$ x 1000 = 29.23

Question 4.
Calculate crude death rate and standardised death rate from the following data:

P – standard population; A ASDR’s

CDR = $$\frac{1470}{110000}$$ x 1000 = 13.36
SDR = $$\frac{1368960}{100000}$$ = 13.68

Question 5.
The following table gives the age and sex composition of population along with the number of live births in an year. Calculate total fertility rate.

TFR = 5 Σ Quinquennial ASFR’s
ASFR

ASFR(15 – 19) = $$\frac{150}{4120}$$ x 1000 = 36.40
TFR= 5 x 542.575 = 2712.875 births per 1000 women.

Question 6.
Calculate total fertility rate :

Total Fertility Rate = EQuinquennial as ASFR

ASFR(15 – 19) = $$\frac{100}{1500}$$ x 1000 = 66.66
TFR= 5 x 764.63 = 3823.15 births per 1000 women.

Question 7.
Write down the components of the life table.

Note: For explanation of components of life table Refer, P. No. 13.

Question 8.
Calculate “Total Fertility Rate” for the following data.

The total fertility rate is:
T.F.R. = 5 x Σ Quinquennial ASFR’s
ASFR

T.F.R. = 5 x 474.93 = 2374.65 Births per 1000 women.

Question 9.
Calculate standarlised death rates from the following data.

Here Death rates means : Age specific death rates of Town A (A) and Town B (B) are given.
So, SDR(A) = $$\frac{\Sigma \mathrm{PA}}{\Sigma \mathrm{P}}$$
SDR(B) $$\frac{\Sigma \mathrm{PB}}{\Sigma \mathrm{P}}$$

SDR(A) = $$\frac{1357000}}{107000}}$$ = 12.68
SDR(B) = $$\frac{1329000}}{107000}}$$ = 12.42

Question 10.
From the following data compute
(i) GF.R.
(ii) A.S.F.R for the age groups (20-29)

$$\frac{1878}{36320}$$ x 1000
GF.R. =51.7
Here women of child bearing age is (15-49) years only.
A.S.F.R for the age group (20-29) in the year

Question 11.
From the following data. Calculate the Standardized Death Rates for Locality A and Locality B.

Since Locality A population is considered as standard so, compute CDR for LocalityA and for Locality B,SDR.

SDR (B) = $$\frac{489780.00}{36000}$$ = 13.605
SDR (B)  = $$\frac{\Sigma \mathrm{PB}}{\Sigma \mathrm{P}}$$; P = Standard popn. (of B), B = ASDR’S
No.of deaths occurring in the year

CDR(A) = $$\frac{420}{36000}$$ x 1000=11.67
For Locality B

SDR (B) = $$\frac{489780.00}{36000}$$ = 13.605

Question 12.
Compute Crude Death Rate and Standardised Death Rate for the following data:

Crude death rate (C.D.R)

S.D.R = $$\frac{\Sigma \mathrm{PA}}{\Sigma \mathrm{P}}$$; Where P – standard population, A – age specific death rate

CDR(A) = $$\frac{3640}{120,000}$$ x 1000 = 30.33
SDR (B) = $$\frac{2,92,000}{95,000}$$ = 30.82

Question 13.
Calculate gross reproduction rate from the following data and comment on population status.

Gross reproduction rate:
G.R.R = (i) $$\sum_{i=15}^{49}$$W.S.F.R
Where i – Age width
W.S.F.R = $$\frac{\text { Female births }}{\text { Female population }}$$ x 1000
W.S.F.R( 15-19) = $$=\frac{80}{8600}$$ x 1000 = 9.38
Similarly calculate for other age groups.

ΣY W.S.F.R = 180.43; i = Age width = 5
∴ G.R.R = 5 x 180.43 = 902.15 Female births per 1000 women of child bearing age.
No. of Female children born per women = $$\frac{\mathrm{G} \cdot \mathrm{R} \cdot \mathrm{R}}{1000}$$
= $$\frac{902.15}{1000}$$ = 0.902
Sience this rate. / value is below one, the papulation decreases.

Question 14.
Calculate net reproduction rate from the data given below and comment on population status.

Nety Production:
N.R.R = (i) $$\sum_{i=15}^{49}$$ W.S.F.R x S
Where i – age width, S-Survival Rates.
W.S.F.R = $$\frac{\text { Femalebirths }}{\text { Female population }}$$ x 1000
W.S.F.R X S(15 – 19) = 25 x 0.96 = 24
Similarly calculate for other age groups

Σ W.S.F.R x S = 596.62
∴ M.R.R = 5 x 596.62 = 2983.09 Female births occur per 1000 women of (15 = 49) years.
N.R.R. per women = $$\frac{\mathrm{N} \cdot \mathrm{R} \cdot \mathrm{R}}{1000}=\frac{2983.09}{1000}= 2.983$$ Female Children bom per women.
Here the N.R.R. per women is more than one.
Therefore, the population increases. [Because the mother will be replaced by daughters so that fertility will be continued].

2nd PUC Statistics Vital Statistics Ten Marks Questions and Answers

Question 1.
From the following data, calculate Total Fertility Rates and compare the fertility of the two cities:

Total Fertility Rate = 5ΣQuinquennial ASFR’s

ASFR(15-19) = $$\frac{1204}{14000}$$ x 1000 = 86.

T.F.R (A) = 5 x 626 = 3130
T.F.R.(B) = 5 x 559 = 2795
Here TFR (A) > TFR (B)
∴ City A is more fertile than City B

Question 2.
Compute Standardised death rates for the two towns and give your comments.

SDR (A) =$$\frac{\Sigma \mathrm{PA}}{\Sigma \mathrm{P}}$$ ; SDR(B) =$$\frac{\Sigma \mathrm{PB}}{\Sigma \mathrm{P}}$$
A = ASDR’s of Town A, B = ASDR’s of Town B, P = Std Population.

SDR (A) = $$\frac{1150000}{40000}$$ = 28. 75 ;
SDR (B) = $$\frac{1175000}{40000}$$ = 29.375
Death rate of Town B is more than Town A. Town A is more healthier than town B.

Question 3.
From the following data, Calculate the standardised death rate for the two populations A and B

Here Death rates are given, i.e., ASDR’s of Population A and B. Let A and B be ASDR’s (Death rates) of Population A and B.
SDR (A) = $$\frac{\Sigma \mathrm{PA}}{\Sigma \mathrm{P}}$$ ; SDR(B) = $$\frac{\Sigma \mathrm{PB}}{\Sigma \mathrm{P}}$$ Where P = Std. Population.

SDR (A) = $$\frac{1556200}{122000}$$ = 28. 75 ;= 12.756;
SDR (B) = 13.269.

Question 4.
Compute the standardised death rates for the following two populations A and B by taking the population A as the standard.

Since Population A is considered as standard Population. So, compute CDR for population A and SDR for Population B.
SDR (A) = CDR(A) = $$\frac{\text { No. of deaths occuring in the year }}{\text { Average Population in the year }}$$ x 1000
SDR (B) = $$\frac{\Sigma \mathrm{PB}}{\Sigma \mathrm{P}}$$ , B ASDR’s of Population B, P = Standard Population of A.
For Population A :
CDR(A) = $$\frac{585}{54000}$$ = 10.83
For Population B

SDR (A) = $$\frac{569550}{54000}$$ = 10.547

Question 5.
From the following data. Calculate standardised death rate for locality A and Locality
B. Which locality is more healthy?

Since Population B is considered as standard Population computing CDR is same as the SDR for Population B. .
SDR (B) = CDR(B) = $$\frac{\text { No. of deaths occuring in the year }}{\text { Average Population in the year }}$$ x 1000
SDR (A) = $$\frac{\Sigma \mathrm{PB}}{\Sigma \mathrm{P}}$$ , B ASDR’s of Population B, P = Standard Population of A.

SDR (A) = $$\frac{38545}{31100}$$ = 3939
CDR (B) = $$\frac{410}{31100}$$ x 1000 = 13.18
Since SDR of A is less in Locality A, it is more healthy.

Question 6.
Calculate standardized death rates from the following data.

Death Rates i.e, ASDR’s for city A and B are given:

SDR (A) = $$\frac{1164000}{97000}$$ = 12
SDR (B) = $$\frac{1213000}{97000}$$ = 12.505

Question 7.
For the following data calculate standardized death rates. Hence find which locality is more healthier.

Let A and B be the ASDR of locality A and Locality B P – the standard population
Then, SDR(A) = $$\frac{\Sigma \mathrm{PA}}{\Sigma \mathrm{P}}$$
SDR (B) = $$\frac{\Sigma \mathrm{PB}}{\Sigma \mathrm{P}}$$

SDR (A) = $$\frac{1945000}{105000}$$ = 18.5238
SDR (B) = $$\frac{1900000}{1050000}$$ = 18.095
Here, SDR(B) < SDR (A)
Locality B is healthier.

Question 8.
From the following table calculate standardised death rates and hence tell which town is healthier (take town B as standard)

Here, Deaths per 1000 population, ie., Age specific death rates of Town A (A) and Town B (B) are given.

∴ Standardised death rate of Town A is –
SDR (A) = $$\frac{83700}{5310}$$ = 15.76
Standardised death rate of Town B is –
SDR (B) = $$\frac{89550}{5310}$$ = 16.86
Here SDR(A) < SDR(B).
.’. Town A is more healthier than Town B.

Question 9.
The Population of a city at the end of 2004 was 4,43,850. There were 10,452 births and 6,845 deaths in 2005. The number of emigrants was 12,435. Estimate the population at the end of 2005. Find crude birth rate and crude death rate.
Given P0= Population at the end of 2004 = 4,43,850.
B= 10,452, D = 6,845, 1 = 44,680, E= 12,435
The estimate of the population at the end of 2005 is – .
Pt= P0+ (B – D) + (I – E)
= 4,43,850 + (10,452 – 6,845) + (44,680 – 12,435)
= 4,79,702

The crude birth rate is –

The crude death rate is –

2nd PUC Basic Maths Question Bank Chapter 5 Partial Fractions Ex 5.2

Students can Download Basic Maths Exercise 5.2 Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 2nd PUC Basic Maths Question Bank Chapter 5 Partial Fractions Ex 5.2

Free Online Partial Fraction Decomposition Calculator. Partial Fraction Calculator.

Part – A

2nd PUC Basic Maths Partial Fractions Ex 5.2 Five Marks Questions and Answers

I. Resolve the following into partial fractions; (3 and 5 marks)

Question 1.
$$\frac{x}{(x+1)(x-4)}$$

Put
x = 4, 4 = A(0) +B (4 + 1) ⇒ 4 = 5B ⇒ B = $$\frac{4}{5}$$
Put x = -1, -1 = A(-1-4) +B(0) ⇒ -1 = -5A = A=$$\frac{1}{5}$$
Substituting both A & B in equation (1) we get

Question 2.
$$\frac{x+1}{(x+2)(x-3)}$$
$$\frac{x+1}{(x+2)(x-3)} =\frac{A}{x+2}+\frac{B}{x-3}$$………………….. (1)
x = 3, 3 + 1 = A(0) +B(3 + 2)
4 = 5B = B = $$\frac{4}{5}$$
Put
x = -2, -2 + 1 = A(-2 – 3) + B(0)
-1 = A(-5)
A = 1/5;
3 = -A ⇒ A = -3

Question 3.
$$\frac{7 x-1}{(1-2 x)(1-3 x)}$$
Let
$$\frac{7 x-1}{(1-2 x)(1-3 x)}=\frac{A}{1-2 x}+\frac{B}{1-3 x}$$
⇒ (7x – 1) = A(1 – 3x) + B(1 – 2x)
Put x = 0, -1 = A + B …………..1
Put x=1 6 = -2A-B …………………….2
Solving 1 & 2 (adding) -A = 5 ⇒ A = -5
B = -1-A = -1 + 5 = 4.

Question 4.
$$\frac{3-7 x^{2}}{(1-3 x)(1+2 x)(1+x)}$$
Let
$$\frac{3-7 x^{2}}{(1-3 x)(1+2 x)(1+x)}=\frac{A}{(1-3 x)}+\frac{B}{1+2 x}+\frac{C}{1+x}$$ …………… (1)
∴ 3 – 7x2 = A(1 + 2x) (1+x) +B(1 – 3x) (1 + x) +C (1 – 3x) (1 + 2x)
Put x = -1, 3 – 7 = A(0) + B(0) +C(1 +3) (1-2)
-4 = -4C ⇒ C = 1
Put x = 0, 3 = A + B + C = A + B = 2
Put x = 1, 3 – 7 = A(1 + 2) (1 + 1) + B(1 – 3) (1 + 1) +C(1 – 3) (1 + 2)
-4 = 6A – 4B – 6C ∵ C= 1
-4 + 6 = 6A – 4B = 2
3A – 2B = 1 2A + 2B = 4
⇒ A + B=2

Question 5.
$$\frac{x^{2}}{(x+1)(x+2)(x+3)}$$
Let $$\frac{x^{2}}{(x+1)(x+2)(x+3)}=\frac{A}{x+1}+\frac{B}{x+2}+\frac{C}{x+3}$$
x2 = A(x +2) (x + 3) +B(x + 1) (x + 3) + C(x + 1) (x + 2)
Put x=-1, (-1)2 = A(-1 +2) (-1 + 3) + 0 + 0
1 = 2A ⇒ A =$$\frac{1}{2}$$
Put x = -2, (-2)2 = A(0) + B(-2 + 1) (-2 + 3) + C(0)
4 = -B ⇒ b = -4
Put x = -3, (-3)2 = A(0) + B(0) +C(-3 + 1) (-3 + 2)
9 = -2C:(-1) ⇒ 9 = 2c ⇒ c = $$\frac{9}{2}$$
Equation 1 be becomes

Question 6.
$$\frac{2 x^{2}+10 x-3}{(x+1)(x-3)(x+3)}$$
Let

2x2 +10x – 3 = A[x – 3) (x + 3) + B(x + 1) (x + 3) + C(x +1) (x – 3)
Put x=-1, 2 – 10 – 3 = A(-4) (2) + B(0) + C(0)
-11 = -8A = A = $$\frac{11}{8}$$
Put x = 3, 18 + 30 – 3 = A(0) + B(4)(6) + C(0)
+45 = 24B ⇒ B = $$\frac{45}{24}=\frac{15}{8}$$
Put x = -3, 18 – 30 – 3 = C(-3 + 1) (-3 -3) = C(-2) (-6)-15 = + 12C
C = $$\frac{-15}{12}=\frac{-5}{4}$$

Question 7.
$$\frac{3 x+1}{x^{2}-6 x+8}$$

Question 8.
$$\frac{x^{2}-10 x+13}{(x+1)\left(x^{2}-5 x+6\right)}$$
Let

x2 – 10x + 13 = A(x-2)(x – 3) + B(x +1) (x – 3) + C(x + 1) (x – 2)
Put x=-1, 1 + 10 + 13 = A (-3) (-4) + 0 + 0
24 = 12A ⇒ A = $$\frac{24}{12}$$=2
Put x = 2, 4 – 20 + 13 A(0) + B(3) (-1) + C(0)
-3 = -3B ⇒ B = 1
Put x = 3, 9 – 30 + 13 = A(0) + B(0) + C(4) (1)
-8 = 47 ⇒ C= -2

Question 9.
$$\frac{3 x+20}{x^{2}+4 x}$$
Let $$\frac{3 x+20}{x^{2}+4 x}=\frac{3 x+20}{x(x+4)}=\frac{A}{x}+\frac{B}{x+4}$$ ……..(1)
3x + 20 = A(x + 4) + B(x)
Put x=0, 20 = 4A ⇒ A = 5
Put x = -4, -12 + 20 = A(0) + B(-4)
8 = -4B ⇒ B = -2
$$\frac{3 x+20}{x^{2}+4 x}=\frac{5}{x}-\frac{2}{x+4}$$

Question 10.
$$\frac{x+3}{(x-1)\left(x^{2}-4\right)}$$
Let $$\frac{x+3}{(x-1)\left(x^{2}-4\right)}=\frac{x+3}{(x-1)(x-2)(x+2)}=\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x+2}$$ ……(1)
(x + 3) = A[x -2) (x + 2) +B(x – 1) (x + 2) + C(x – 1) (x – 2)
Put x= 1, 4 = A(-1)(3) ⇒ A=$$\frac{-4}{3}$$
Put x = 2, 5 = A(0) + B(1) (4) + C(O)
Put 5 = 4B ⇒ B = $$\frac{-4}{3}$$
Put x = -2, -2 + 3 = A(0) + B(0) +C(-3) (-4)
1 = 12C ⇒ C = $$\frac{1}{12}$$

Question 11.
$$\frac{x+3}{x^{3}-x}$$
Let $$\frac{x+3}{x^{3}-x}=\frac{x+3}{x(x-1)(x+1)}=\frac{A}{x}+\frac{B}{x-1}+\frac{C}{x+1}$$ ….. (1)
x + 3 = A(x-1) (x + 1) + B(x) (x + 1) + C(x) (x – 1)
Put x = 0 3 = -A + 0 + 0 ⇒ A=-3
Put x = 1, 4 = A(0) + B(1) (2) + 0 = 4 = 2B ⇒ B = 2
Put x = -1, 2 = A(0) + B(0) + C(-1) (-2); 2 = 2c ⇒ c = 1
∴ $$\frac{x-3}{x^{3}-x}=\frac{-3}{x}+\frac{2}{x-1}+\frac{1}{x+1}$$

Question 12.
$$\frac{1+3 x+2 x^{2}}{(1-2 x)\left(1-x^{2}\right)}$$
Let

1 + 3x + 2x2 = A(1 – x)(1 + x) +B(1 – 2x)(1 + x) + C(1 – 2x) (1 – x)
Put x = 1, 6 = A(0) + B(-1)(2) +C(0);
6 = -2B ⇒ B = -3
Put x=-1, 0) = A(0) + B(0) +C(1 + 2)(2)
6C = 0 ⇒ C = 0
Put x = 0, 1 = A + B + C = A – 3 = 1 ⇒ A = 1 + 3 = 4

Part – B

1. Resolve the following into partial fractions; (5 Marks)

Question 1.
$$\frac{4}{(x-3)(x+1)^{2}}$$
Let $$\frac{4}{(x-3)(x+1)^{2}}=\frac{A}{x-3}+\frac{B}{x+1}+\frac{C}{(x+1)^{2}}$$
∴4 = A(x + 1)2 + B(x + 1)(x – 3) + C(x – 3)
Put x = 3, 4 = A(4)2 + B(0) + C(0)
4 = 16A ⇒ A = $$\frac{1}{4}$$
Put x =-1, 4 = A(0) + B(0) + C(-1-3); Put 4 = -4C ⇒ C = -1
Put x = 0 4 = A- 3B – 3C
3B = A – 3C – 4

Question 2.
$$\frac{9}{(x+1)(x+2)^{2}}$$
Let $$\frac{9}{(x+1)(x+2)^{2}}=\frac{A}{x+1}+\frac{B}{x+2}+\frac{C}{(x+2)^{2}}$$
9 = A(x + 2)2 + B(x + 1)(x + 2) +C(x + 1)
Put x = -1, 9 = A(-1 + 2)2 + 0 + 0
A = 9
Put x= -2, 9 = A(0) + B(0) + CC – 10 = -9
Put x = 0, 9 = 4A + 2B + C
9 = 36 + 2B -9
9 = 27 + 2B $$\frac{-18}{2}$$ = B B = -9
∴ $$\frac{9}{x-1}-\frac{9}{x+2}-\frac{9}{(x+1)^{2}}$$

Question 3.
$$\frac{3 x+4}{(x+1)^{2}(x-1)}$$
Let $$\frac{3 x+4}{(x+1)^{2}(x-1)}=\frac{A}{x+1}+\frac{B}{(x+1)^{2}}+\frac{C}{x-1}$$
3x+4 = A(x + 1)(x – 1) + B(x – 1) + C (x + 1)2
Put x = -1, ⇒ 3 + 4 = A(0) + B(-2) + C(0)
1 = -2B ⇒ B = $$-\frac{1}{2}$$
Put x = 1, = 3 + 4 = A(0) +B(0) + C(2)2
7 = 4C ⇒ C = 5
Comparing the coefficients of x2 on both sides
0 = A +C ⇒ A = -C = $$-\frac{7}{4}$$

Question 4.
$$\frac{3 x+2}{(x-2)(x+3)^{2}}$$
Let $$\frac{3 x+2}{(x-2)(x+3)^{2}}=\frac{A}{x-2}+\frac{B}{x+3}+\frac{C}{(x+3)^{2}}$$
(3x + 2) = A(x + 3)2 + B(x – 2) (x + 3) + C(x – 2)
Put x = 2, 6 + 2 = A(2 + 3)2 + B(0)+C (0)
8 = 25A ⇒ A = $$\frac{8}{25}$$
Put X=-3, -9 + 2 = A(0) + B(0) +C(-5)
-7 = -5C ⇒ C = $$\frac{7}{5}$$
Comparing the co-efficients of x2 on both sides
0 = A + B ⇒ B = -A = $$\frac{8}{25}$$

Question 5.
$$\frac{2 x^{2}-4 x+1}{(x+2)(x-3)^{2}}$$
2x2 – 4x + 1 = A[x – 3)2 + B(x – 2) (x-3) + C (x – 2)
Put x = 2, 8-8 + 1 = A(-1)2 = A = 1
Put x = 3, 18 – 12 + 1 = A(0) + B(0) + C(3 – 2) = 7 = C
Comparing coefficient of x2 = 2 = A + B = B = 2-A = 2 -1 =1
∴ $$\frac{2 x^{2}-4 x+1}{(x-2)(x-3)^{2}}=\frac{1}{x-2}+\frac{1}{x-3}+\frac{7}{(x-3)^{2}}$$

Question 6.
$$\frac{x^{2}}{(x+1)^{2}(x-5)}$$
Let $$\frac{x^{2}}{(x+1)^{2}(x-5)}=\frac{A}{x+1}+\frac{B}{(x+1)^{2}}+\frac{C}{x-5}$$
x2 = A (x + 1)(x – 5) + B(x – 5) + C(x + 1)2
Put x = -1, 1 = A(0) + B(-1-5) + C(0)
1 = -6B ⇒ B = $$-\frac{1}{6}$$
Put x = 5, 25 = A(0) + B(0) + C(6)2
C = $$\frac{25}{36}$$
Compare the coefficients of x2 on both sides we get

Question 7.
$$\frac{4-7 x}{(2+3 x)(1+x)^{2}}$$
Let $$\frac{4-7 x}{(2+3 x)(1+x)^{2}}=\frac{A}{2+3 x}+\frac{B}{1+x}+\frac{C}{(1+x)^{2}}$$
⇒ 4 – 7x = A(1 + x)2 +B(1 + x) (2 + 3x) + C(2 + 3x)
Put x=-1, 11 = A(0) + B(0) + C(-1)
C = -11
Put x = 0 4 = A + 2B + 2C ⇒ 26 = A + 2B …..(1)
Compare the coefficients off of x2 on both sides
0 = A + 3B …….(2)
Equations 1 – 2 gives 26 =-B = 0 ⇒B = -26& A = 78
∴ $$\frac{4-7 x}{(2+3 x)(1+x)^{2}}=\frac{78}{2+3 x}-\frac{26}{1+x}-\frac{11}{(1+x)^{2}}$$

Question 8.
$$\frac{1+2 x}{(x+2)^{2}(x-1)}$$
Let $$\frac{1+2 x}{(x+2)^{2}(x-1)}=\frac{A}{x+2}+\frac{B}{(x+2)^{2}}+\frac{C}{x-1}$$
1 + 2x = A (x + 2) (x – 1) + B(x – 1) +C(x + 2)2
3 = A(0) + B(0) + C(9) ⇒ C = $$\frac{1}{3}$$
Put x = -2, 1 – 4 = B(-3) ⇒ B = 1
Comparing the coefficient of x2 on both sides we get

Question 9.
$$\frac{9 x-27}{(2+1)(x-2)^{2}}$$
Let $$\frac{9 x-27}{(2+1)(x-2)^{2}}=\frac{A}{x+1}+\frac{B}{x-2}+\frac{C}{(x-2)^{2}}$$
9x – 27 = A(x – 2)2 + B(x + 1)(x – 2) + C(x + 1)
Put x = -1, -36 = A(-3)2 + B(0) + C(0)
-36 = 9A ⇒ A=-4
Put x = 2, 18 – 27 = A(0) + B(0) +C(2+1)
-9 = 3C ⇒ C =-3
Comparing the coefficients of x? on both sides
0 = A + B = B = -A ⇒ B =-(-4) = 4

Question 10.
$$\frac{2 x+5}{(x+2)(x-1)^{2}}$$
Let $$\frac{2 x+5}{(x+2)(x-1)^{2}}=\frac{A}{x+2}+\frac{B}{x-1}+\frac{C}{(x-1)^{2}}$$
2x + 5 = A(x – 1)2 + B(x – 1)(x + 2) +C(x + 2)
Put x = -2, -4 + 5 = A(-3)2 + 0 + 0
1 = 9A ⇒ A =$$\frac{1}{9}$$
Put x= 1, 2 + 5 = A(0) + B(0) + C(1 + 2)
7 = 3C ⇒ C = $$\frac{7}{3}$$
Comparing the coeff of x2 on both sides
0 = A+B ⇒ B = A = $$-\frac{1}{9}$$

Question 11.
$$\frac{x}{(1+2 x)^{2}(1-3 x)}$$
Let $$\frac{x}{(1+2 x)^{2}(1-3 x)}=\frac{A}{1+2 x}+\frac{B}{(1+2 x)^{2}}+\frac{C}{1-3 x}$$
X = A(1 + 2x) (1 – 3x) + B(1 – 3x) + C(1 + 2x)2
Put x = 0 we get A + B + C = 0
Comparing co efficient of x2 both sides
0 = -6A + 40 ⇒ 6A = 4C ⇒3A = 20
We have A+B+C = 0
⇒ 3A + 3B + 3C = 0
2C + 3B + 3C = 0
5C = -3B
: 3A = 2C
Comparing the coefficient of x both sides

Part – C

III. Resolve into partial fractions: (5 Marks)

Question 1.
$$\frac{2 x^{2}-7 x+1}{x^{2}-3 x-4}$$
$$\frac{2 x^{2}-7 x+1}{x^{2}-3 x-4}$$
This is an improper fraction
∴ Convert into proper fraction by actual division.

9- x = A(x + 1) + B(x – 4)
Put x = 4, 9-4 = A(4 + 1) + B(0)
5 = 5A ⇒ A = 1
Put x=-1, 9-(-1) = A(0) +B(-1-4)
10 = -5B ⇒ B = -2

Question 2.
$$\frac{4 x^{2}-3 x+5}{(2-x)(1+x)}$$

x + 13 = A(1 + x) + B(2 – x)
Put x = 2, 15 = A[1 + 2) + B(0)
15 = 3A ⇒ A = $$\frac{15}{3}$$ = 5
Put x=-1, -1 + 13 = A(0) +B(2-(-1))
12 = 3B ⇒ B = 4

Question 3.
$$\frac{x^{3}+7 x^{2}+17 x+11}{x^{2}+5 x+6}$$

(x – 1) = A(x + 3) + B(x + 2)
Put x = -2, -3 = A(-2 + 3) + B(0)
-3 = A ⇒ A=-3
Put X=-3, -4 = A(0) + B(-3 + 2)
-4 = -B ⇒ B = 4

Question 4.
$$\frac{2 x^{2}+3 x+2}{x^{2}-x-2}$$

∴ 5x + 6 = A (x + 1) +B(x – 2)
Put x = 2, 16 = A(3) ⇒ A = $$\frac{16}{3}$$
Put x = -1, 1 = A(0) + B(-3)=B = $$\frac{1}{-3}$$
1 2x+3x+2-21 16 1 x – x – 2 =2+3(x-2) 3(x+1)

Question 5.
$$\frac{2 x^{3}+x^{2}-x-3}{x(x-1)(2 x+3)}$$

∴ 2x – 3 = A[x -1) (2x + 3) +B(x) (2x + 3) + C(x) (x – 1)
Put x = 0 -3 = A(-1) (3) + B(0) + C(0)
-3 = -3A ⇒ A = 1
Put x = 1, -1 = A(0) + B(1) (2 + 3) + C(0)
-1 = 5B ⇒ B = $$-\frac{1}{5}$$
Compare the co-efficient of x2 both sides

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 Section Questions to be given Questions to be answered A 12 10 B 12 10 C 10 7 D 6 4 E 3 2 Total 43 33

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 1 Knowledge Questions relating to simple meanings, one-word answers, years, expansion of abbreviations, very short answers. 2 Understanding Questions relating to Definitions, meanings, short answers, long and essay-type answers requiring explanations like features, importance, benefits, etc. 3 Application Multiple Choice Questions and questions relating to examples, answers requiring contrast, distinction or comparison, sequential steps/procedure involved in a process. etc. 4 Skill Diagrams, Practical Oriented Questions

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