Problems on Ages Questions and Answers

Q: The sum of the present ages of a father and his son is 60 years. Five years ago, father's age was four times the age of the son, so now the son's age will be

The son's present age is 15 years.Let the son be S, so the father is 60 - S. Five years ago the father was four times the son:\[ \begin{aligned} 60 - S - 5 &= 4(S - 5) \\ 55 - S &= 4S - 20 \\ 75 &= 5S \Rightarrow S = 15 \end{aligned} \]Check: the father is 45; five years ago they were 40 and 10, and 40 is four times 10. 5 and 10 are ages five or ten years earlier, and 20 fails the check.

Q: Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7 : 9, find the age of Sachin.

Sachin is 24.5 years old.With the ratio 7 : 9, the ages are 7k and 9k, and their difference 2k equals 7 years:\[ \begin{aligned} 9k - 7k &= 7 \Rightarrow k = 3.5 \\ \text{Sachin} &= 7 \times 3.5 = 24.5 \end{aligned} \]Rahul is then 31.5, and 24.5 : 31.5 = 7 : 9. The other options give differences that do not match the ratio; 27.5, for example, would make Rahul 34.5, a ratio of about 0.8.

Q: The present ages of A and B are in the ratio 5 : 4. Two years ago the ratio of their ages was 4 : 3. What is the present age of A ?

A's present age is 10 years.Let the present ages be 5x and 4x. Two years ago they were 5x - 2 and 4x - 2, in the ratio 4 : 3:\[ \begin{aligned} 3(5x - 2) &= 4(4x - 2) \\ 15x - 6 &= 16x - 8 \\ x &= 2 \end{aligned} \]So A is 5 × 2 = 10 years old and B is 8. Two years ago they were 8 and 6, which is 4 : 3. The option of 8 years is B's age, not A's, and 12 years does not satisfy the second ratio.

Q: A is two years older than B who is twice as old as C. If the total of ages of A, B, C is 27, then how old is the B?

B is 10 years old.Let C be \(x\). Then B is \(2x\) and A is \(2x + 2\):\[ \begin{aligned} (2x + 2) + 2x + x &= 27 \\ 5x &= 25, \quad x = 5 \end{aligned} \]So C is 5, B is 10 and A is 12. 12 is A's age, the usual slip of answering for the wrong person, and 8 and 14 do not satisfy the total.

Q: Sudha's grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. Eight years ago, what was the ratio of Sudha's age to that of her grandfather ?

The ratio is 11 : 53.Let Sudha be \(S\) and her grandfather \(G\) years old now.\[ \begin{aligned} G - 16 &= 8(S - 16) \Rightarrow G = 8S - 112 \\ G + 8 &= 3(S + 8) \Rightarrow G = 3S + 16 \\ 8S - 112 &= 3S + 16 \Rightarrow S = 25.6 \end{aligned} \]Then \(G = 92.8\). Eight years ago they were 17.6 and 84.8:\[ \frac{17.6}{84.8} = \frac{176}{848} = \frac{11}{53} \]The ages are not whole numbers, but the ratio is exact. The neater ratios 1 : 5 and 3 : 8 do not satisfy both conditions.

Q: The sum of ages of a father and a daughter is 80 years now. If 10 years ago the ratio was 2:1, then after 10 years the ratio of their ages will be:

After 10 years the ratio will be 3:2.Let the father's age be \(F\) and the daughter's \(D\), so \(F + D = 80\). Ten years ago their ages were in the ratio 2:1:\[ \begin{aligned} F - 10 &= 2(D - 10) \\ (F - 10) + (D - 10) &= 60 \\ 3(D - 10) &= 60 \\ D &= 30,\ F = 50 \end{aligned} \]After 10 years they will be 60 and 40, a ratio of 60:40 = 3:2.5:3 is their present ratio (50:30), the usual slip of forgetting to add the 10 years.

Q: The present age of A and B are in the ratio 4 : 5 and after five years they will be in the ratio 5 : 6 then their sum of present age is

The sum of their present ages is 45 years.Let the ages be \(4x\) and \(5x\). After five years,\[ \begin{aligned} \frac{4x + 5}{5x + 5} &= \frac{5}{6} \\ 24x + 30 &= 25x + 25 \Rightarrow x = 5 \end{aligned} \]So the ages are 20 and 25, totalling 45. Check: in five years they are 25 and 30, in the ratio 5 : 6. 55 years is their total after five years (25 + 30), and 35 and 25 do not fit.

Q: Rahul is 4 years younger than his elder brother Shyam. Rahul also has a sister who is 3 years younger to him. What is the difference between the age of Rahul and the average age of the; three siblings?

The difference is 4 months.Let Rahul's age be \(R\). Shyam is \(R + 4\) and the sister \(R - 3\).\[ \begin{aligned} \text{average} &= \frac{(R+4) + R + (R-3)}{3} \\ &= R + \tfrac{1}{3} \end{aligned} \]The average is a third of a year, 4 months, more than Rahul's age. 6 months and 8 months come from slips in adding the two differences (+4 and -3, net +1).

Q: Reshmi is 12 years younger than Sruti. Reshmi's age is 40% of the sum of her and Sruti's age. What will be Sruti's age after 9 years hence ?

Sruti will be 45 years old after 9 years.Let Sruti's age be \(s\), so Reshmi's is \(s - 12\). Reshmi's age is 40% of their total:\[ \begin{aligned} s - 12 &= 0.4(2s - 12) \\ s - 12 &= 0.8s - 4.8 \\ 0.2s &= 7.2,\ s = 36 \end{aligned} \]So Sruti is 36 now and Reshmi 24 (check: 24 is 40% of 60). After 9 years Sruti will be \(36 + 9 = 45\). 36 is her present age, the answer before adding the 9 years; 25 matches neither person at any point.

Important Instructions

11.

The sum of the present ages of a father and his son is 60 years. Five years ago, father's age was four times the age of the son, so now the son's age will be

A.5
B.10
C.15
D.20

Exam Year(s)

MPPSC State Service - 2022, MPPSC Forest Service - 2022,

Answer: C

The son's present age is 15 years.

Let the son be S, so the father is 60 - S. Five years ago the father was four times the son:

\[ \begin{aligned} 60 - S - 5 &= 4(S - 5) \\ 55 - S &= 4S - 20 \\ 75 &= 5S \Rightarrow S = 15 \end{aligned} \]

Check: the father is 45; five years ago they were 40 and 10, and 40 is four times 10. 5 and 10 are ages five or ten years earlier, and 20 fails the check.

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12.

Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7 : 9, find the age of Sachin.

A.24.5
B.25.5
C.26.5
D.27.5

Exam Year(s)

MPPSC State Service - 2022, MPPSC Forest Service - 2022,

Answer: A

Sachin is 24.5 years old.

With the ratio 7 : 9, the ages are 7k and 9k, and their difference 2k equals 7 years:

\[ \begin{aligned} 9k - 7k &= 7 \Rightarrow k = 3.5 \\ \text{Sachin} &= 7 \times 3.5 = 24.5 \end{aligned} \]

Rahul is then 31.5, and 24.5 : 31.5 = 7 : 9. The other options give differences that do not match the ratio; 27.5, for example, would make Rahul 34.5, a ratio of about 0.8.

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13.

The present ages of A and B are in the ratio 5 : 4. Two years ago the ratio of their ages was 4 : 3. What is the present age of A ?

A.8 years
B.9 years
C.10 years
D.12 years

Exam Year(s)

MPPSC State Service - 2023, MPPSC Forest Service - 2023,

Answer: C

A's present age is 10 years.

Let the present ages be 5x and 4x. Two years ago they were 5x - 2 and 4x - 2, in the ratio 4 : 3:

\[ \begin{aligned} 3(5x - 2) &= 4(4x - 2) \\ 15x - 6 &= 16x - 8 \\ x &= 2 \end{aligned} \]

So A is 5 × 2 = 10 years old and B is 8. Two years ago they were 8 and 6, which is 4 : 3. The option of 8 years is B's age, not A's, and 12 years does not satisfy the second ratio.

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14.

A is two years older than B who is twice as old as C. If the total of ages of A, B, C is 27, then how old is the B?

A.10
B.12
C.14
D.8

Exam Year(s)

Northern Coalfields Limited - 2020, NCL Technician - 2020,

Answer: A

B is 10 years old.

Let C be \(x\). Then B is \(2x\) and A is \(2x + 2\):

\[ \begin{aligned} (2x + 2) + 2x + x &= 27 \\ 5x &= 25, \quad x = 5 \end{aligned} \]

So C is 5, B is 10 and A is 12. 12 is A's age, the usual slip of answering for the wrong person, and 8 and 14 do not satisfy the total.

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15.

Sudha's grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. Eight years ago, what was the ratio of Sudha's age to that of her grandfather ?

A.11 : 53
B.3 : 8
C.1 : 5
D.1 : 2

Exam Year(s)

Punjab Civil Service - 2025,

Answer: A

The ratio is 11 : 53.

Let Sudha be \(S\) and her grandfather \(G\) years old now.

\[ \begin{aligned} G - 16 &= 8(S - 16) \Rightarrow G = 8S - 112 \\ G + 8 &= 3(S + 8) \Rightarrow G = 3S + 16 \\ 8S - 112 &= 3S + 16 \Rightarrow S = 25.6 \end{aligned} \]

Then \(G = 92.8\). Eight years ago they were 17.6 and 84.8:

\[ \frac{17.6}{84.8} = \frac{176}{848} = \frac{11}{53} \]

The ages are not whole numbers, but the ratio is exact. The neater ratios 1 : 5 and 3 : 8 do not satisfy both conditions.

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16.

The sum of ages of a father and a daughter is 80 years now. If 10 years ago the ratio was 2:1, then after 10 years the ratio of their ages will be:

A.3:2
B.5:3
C.5:4
D.4:3

Exam Year(s)

RSMSSB - 2026, RSMSSB Mahila Supervisor - 2026,

Answer: A

After 10 years the ratio will be 3:2.

Let the father's age be \(F\) and the daughter's \(D\), so \(F + D = 80\). Ten years ago their ages were in the ratio 2:1:

\[ \begin{aligned} F - 10 &= 2(D - 10) \\ (F - 10) + (D - 10) &= 60 \\ 3(D - 10) &= 60 \\ D &= 30,\ F = 50 \end{aligned} \]

After 10 years they will be 60 and 40, a ratio of 60:40 = 3:2.

5:3 is their present ratio (50:30), the usual slip of forgetting to add the 10 years.

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17.

The present age of A and B are in the ratio 4 : 5 and after five years they will be in the ratio 5 : 6 then their sum of present age is

A.55 years
B.45 years
C.35 years
D.25 years

Exam Year(s)

TNPSC Group 1 - 2017, TNPSC - 2017,

Answer: B

The sum of their present ages is 45 years.

Let the ages be \(4x\) and \(5x\). After five years,

\[ \begin{aligned} \frac{4x + 5}{5x + 5} &= \frac{5}{6} \\ 24x + 30 &= 25x + 25 \Rightarrow x = 5 \end{aligned} \]

So the ages are 20 and 25, totalling 45. Check: in five years they are 25 and 30, in the ratio 5 : 6. 55 years is their total after five years (25 + 30), and 35 and 25 do not fit.

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18.

Mary is 16 years old. She is 4 times older than her brother. How old will she be when she is twice his age?

A.20
B.24
C.28
D.32

Exam Year(s)

TNPSC Group 1 - 2025, TNPSC - 2025,

Answer: B

Mary is 16 and her brother is 16 / 4 = 4 years old, a difference of 12 years.

She is twice his age when \[16+x=2(4+x)\Rightarrow x=8,\] so Mary is 24 then, option B. Check: her brother is 12, and 24 is twice 12.

Her brother is 4 and the age gap of 12 years stays the same, so she is twice his age when his age equals the 12-year gap, that is at 12 and 24.

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19.

Rahul is 4 years younger than his elder brother Shyam. Rahul also has a sister who is 3 years younger to him. What is the difference between the age of Rahul and the average age of the; three siblings?

A.6 months
B.4 months
C.2 months
D.8 months

Exam Year(s)

Tripura Public Service Commission - 2025,

Answer: B

The difference is 4 months.

Let Rahul's age be \(R\). Shyam is \(R + 4\) and the sister \(R - 3\).

\[ \begin{aligned} \text{average} &= \frac{(R+4) + R + (R-3)}{3} \\ &= R + \tfrac{1}{3} \end{aligned} \]

The average is a third of a year, 4 months, more than Rahul's age. 6 months and 8 months come from slips in adding the two differences (+4 and -3, net +1).

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20.

Reshmi is 12 years younger than Sruti. Reshmi's age is 40% of the sum of her and Sruti's age. What will be Sruti's age after 9 years hence ?

A.25
B.36
C.45
D.None of these

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: C

Sruti will be 45 years old after 9 years.

Let Sruti's age be \(s\), so Reshmi's is \(s - 12\). Reshmi's age is 40% of their total:

\[ \begin{aligned} s - 12 &= 0.4(2s - 12) \\ s - 12 &= 0.8s - 4.8 \\ 0.2s &= 7.2,\ s = 36 \end{aligned} \]

So Sruti is 36 now and Reshmi 24 (check: 24 is 40% of 60). After 9 years Sruti will be \(36 + 9 = 45\). 36 is her present age, the answer before adding the 9 years; 25 matches neither person at any point.

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