Problems on Ages PYQs for UPSC (2011-2024) | Solved Questions & PDF Download

Master Age-Based Problems for UPSC with solved Previous Year Questions (PYQs) from 2011 to 2024. This comprehensive guide provides step-by-step solutions, shortcut methods, and a free downloadable PDF to help you solve age-related problems in UPSC CSAT.

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Why Age Problems Matter in UPSC CSAT?

Age-based questions are frequently asked in UPSC CSAT (Paper II) to test:

Q1. A father is nine times as old as his son and the mother is eight times as old as the son. The sum of the father's and the mother's age in 51 years. What is the age of the son? [CSAT 2015]

(a) 7 years

(b) 5 years

(c) 4 years

(d) 3 years

Solution:

Given that,

A father is nine times as old as his son and the mother is eight times as old as the son.

The sum of the father's and the mother's age in 51 years.

Now,

Let the age of Son be S

Age of father = 9S

Age of mother  =8S

9S + 8S = 51

S = 3

Thus the age of the son is 3 years

Hence option (d) is correct

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Q2. The monthly incomes of X and Y are in the ratio of 4:3 and their monthly expenses are in the ratio of 3: 2. However, each saves Rs. 6,000 per month. What is their total monthly income? [CSAT 2017]

(a) Rs. 28,000

(b) Rs. 42,000

(c) Rs. 56,000

(d) Rs. 84,000

Solution:

Given that,

The monthly incomes of X and Y are in the ratio of 4:3 and their monthly expenses are in the ratio of 3:2

Each saves Rs. 6,000 per month.

Now,

Let income be I and expenses be E

Income = 4I : 3I

Expenses = 3E : 2E

4I - 3E = 6000.....(i)

3I - 2E = 6000.....(ii)

Thus by solving the equation (i) and (ii)

I = E = 6000

Therefore, income of X = 4 x 6000 = 24000

Income of Y = 3 x 6000 = 18000

Total income = 24000 + 18000 = 42000

Hence option (b) is correct

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Q3. The age of Mr. X last year was the square of a number and it would be the cube of a number next year. What is the least number of years he must wait for his age to become the cube of a number again? [CSAT 2017]

(a) 42

(b) 38

(c) 25

(d) 16

Solution:

Given that,

The age of Mr. X last year was the square of a number and it would be the cube of a number next year.

Now,

Assuming the age of last year  which is a square can be  1, 4, 9, 16, 25, 36.....

After 2 years the age is cube

After 2 years age will be 3, 6, 11, 18, 27, 38....

Thus age last year was 25 and next year will be 27 and present age is 26

Again the age will be cube = 64

Difference 64 - 26 = 38

Thus it will take 38 years

Hence option (b) is correct

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Q4. Ena was born 4 years after her parents’ marriage. Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old. At what age did Ena's father get married?[CSAT 2019)

(a) 22 years

(b) 23 years

(c) 24 years

(d) 25 years

Solution:

Given that,

Ena was born 4 years after her parents’ marriage.

Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old.

Now,

Ena's age = 13

Mother's age = 24 + 13 = 37 years

Fathers age = 40

Then,

Ena's father age during marriage = 40 - (13 + 4) = 23 years

Hence option (b) is correct

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Q5. In 2002, Meenu's age was one-third of the age of Meera, whereas in 2010, Meenu's age was half the age of Meera. What is Meenu's year of birth? [CSAT 2019]

(a) 1992

(b) 1994

(c) 1996

(d) 1998

Solution:

Given that,

In 2002, Meenu's age was one-third of the age of Meera, whereas in 2010, Meenu's age was half the age of Meera.

Now,

Let meera age in 2002 be A

Meenu age in 2002 = A/3

In 2010

Meera age = A + 8

Meenu age  = (A/3) + 8

Also,

(1/2) x (A + 8) = [(A/3) + 8]

A/2 + 4 = A/3 + 8

A/6 = 4

A = 24

Meenu age = 24/3 = 8

Year of birth = 2002 - 8 = 1994

Hence option (b) is correct

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Q6. X said to Y, "At the time of your birth I was twice as old as you are at present." If the present age of X is 42 years, then consider the following statements:

1. 8 years ago, the age of X was five times the age of Y.

2. After 14 years, the age of X would be two times the age of Y.

Which of the above statements is/are correct? [CSAT 2021]

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

Solution:

Given that,

X said to Y, "At the time of your birth I was twice as old as you are at present." 

The present age of X is 42 years

Now,

Let the age of Y be a years

Age of X = 42 - a

Also, Age of  X  = 2a

42 - a  = 2a

a = 14 years

Present age of Y = 14 Years

1. 8 years ago, the age of X was five times the age of Y.

8 years ago age of Y = 14 - 8 = 6 years

Age of X = 42 - 8 = 34 years

Hence statement 1 is incorrect

2. After 14 years, the age of X would be two times the age of Y.

After 14 years age of Y = 14 + 14 = 28 years

Age of X = 42 + 14 = 56

X = 2Y

Hence statement 2 is correct

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Q7. Consider the Question and two Statements given below: [CSAT 2022]

Question: What is the age of Manisha?

Statement-1: Manisha is 24 years younger than her mother.

Statement-2: 5 years later, the ages of Manisha and her mother will be in the ratio 3:5.

Which one of the following is correct in respect of the Question and the Statements?

(a) Statement-1 alone is sufficient to answer the Question.

(b) Statement-2 alone is sufficient to answer the Question.

(c) Both Statement-1 and Statement-2 are sufficient to answer the Question.

(d) Both Statement-1 and Statement-2 are not sufficient to answer the question.

Solution:

Given that,

Statement-1: Manisha is 24 years younger than her mother.

Statement-2: 5 years later, the ages of Manisha and her mother will be in the ratio 3:5.

Now,

Let the age of Manisha be A and Mother be B

B = 24 + A.....(i)

Statement 1 alone is not sufficient

(B + 5)/(A + 5) = 5/3....(ii)

Statement 2 alone is not sufficient

Combining both statements

Replacing the value of B from equation (i)

(A + 29)/(A + 5) = 5/3

3A + 87 = 5A + 25

2A = 62

A = 31 years

B = 31 + 24 = 56 years

Hence, Both Statement-1 and Statement-2 are sufficient to answer the Question.

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Q8. Consider the following statements: [CSAT 2023]

1. A is older than B.

2. C and D are of the same age.

3. E is the youngest.

4. F is younger than D.

5. F is older than A.

How many statements given above are required to determine the oldest person/persons?

(a) Only two

(b) Only three

(c) Only four

(d) All five

Solution:

Given that,

1. A is older than B.

2. C and D are of the same age.

3. E is the youngest.

4. F is younger than D.

5. F is older than A.

Now,

A > B

C = D

E is the youngest

D > F

C = D > F > A > B > E

Thus all five statements required to answer the question

Hence option (d) is correct

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Q9. A father said to his son, "n years back I was as old as you are now. My present age is four times your age n years back". If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages? [CSAT 2024]

(a) 30 years

(b) 32 years

(c) 34 years

(d) 36 years

Solution:

Given that,

Father age is equivalent to son's present age n years back

Fathers age is 4 times son's age n years back

Sum of fathers age and Sons age is 130 years

Now,

Let the present age of Father and son be F and S

F - n = S......(i)

F =  4 x (S - n).....(ii)

F + S = 130......(iii)

Solving equation (i) and (ii)

F = S + n

S + n = 4S - 4n

5n = 3S

n = 3S/5

So, F = 8S/5......(iv)

Putting the value of equation (iv) in (iii)

(8S/5) + S = 130

13S = 130  x 5

S = 50 years

Thus,  F = 130 - 50 = 80 years

Difference between their ages = 80 - 50 = 30 years

Hence option (a) is correct

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Q10. A Question is given followed by two Statements I and II. Consider the Question and the Statements. [CSAT 2024]

Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q.

Question: What is the difference of their ages?

Statement-l: The age of P is greater than the age of Q.

Statement-II: The sum of their ages is 11/6 times their difference.

Which one of the following is correct in respect of the above Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone

(b) The Question can be answered by using either Statement alone

(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

(d) The Question cannot be answered even by using both the Statements together

Solution:

Given that,

Age of P and Q is less than 100 years but more than 10 years.

Digits of P when interchanged the number represents Q

Statement I:  The age of P is greater than the age of Q.

Statement II: The sum of their ages is 11/6 times their difference.

Now,

let P = 10x + y (two digit number)

Q = 10y + x

Statement I:  The age of P is greater than the age of Q.

10x + y > 10y + x

However, the difference in ages cannot be determined

Hence statement I is insufficient to answer the question

Statement II: The sum of their ages is 11/6 times their difference.

10x + y + 10y + x = (11/6) x (10x + y - 10y - x)

11x + 11y = (11/6) x (9x - 9y)

By solving the equation,

x = 5y

If x = 1, y =5

x = 2, y = 10 (not possible as x and y are single digit integers)

So P and Q will be 15 and 51

Difference in the ages = 51 - 15 = 36 years

Hence statement II is sufficient to answer the question.

Hence option (a) is correct

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ANSWER KEY

• 1.      D
• 2.      B
• 3.      B
• 4.      B
• 5.      B
• 6.      B
• 7.      C
• 8.      D
• 9.      A
• 10.  A

 

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FAQs on Age Problems for UPSC