Problems on Ages Questions and Answers

Q: Eighteen years ago, the ratio of P's age to Q's age was 8:13. Their present age ratios are 5:7. Then the present age of P is

P's present age is 50 years.Let the present ages be \(5x\) and \(7x\). Eighteen years ago they were in the ratio 8:13.\[ \begin{aligned} \frac{5x - 18}{7x - 18} &= \frac{8}{13} \\ 65x - 234 &= 56x - 144 \\ 9x &= 90,\ x = 10 \end{aligned} \]So P is \(5 \times 10 = 50\) and Q is 70. Check: 18 years ago they were 32 and 52, and \(32:52 = 8:13\). 70 years is Q's age, not P's.

Q: The ratio of the present age of father to that of son is 7:2. After 10 years their ages will be in the ratio of 9:4. The present age of father is

The father's present age is 35 years.Let the present ages be \(7k\) and \(2k\). After 10 years:\[ \begin{aligned} \frac{7k + 10}{2k + 10} &= \frac{9}{4} \\ 28k + 40 &= 18k + 90 \\ k &= 5 \end{aligned} \]So the father is 35 and the son 10. Check: in 10 years they will be 45 and 20, and 45 : 20 = 9 : 4. 40, 30 and 25 are not multiples of 7, so none of them can be the father's share of a 7 : 2 ratio in whole years.Ratio questions on ages are solved by writing the present ages as multiples of one unknown and using the fact that every age changes by the same number of years.

Q: A father tells his son, "I was of your present age when you were born". If the father is 36 now, how old was the boy five years back ?

The boy was 13 five years ago.The father's age when the son was born equals the son's present age, \(s\). The father is that much older than the son, so his present age is \(s + s = 2s\):\[ \begin{aligned} 2s &= 36 \\ s &= 18 \end{aligned} \]Five years ago the boy was \(18 - 5 = 13\). 18 would be his present age, which is not what is asked, and 15, 17 and 20 do not follow.Check: the son is 18 and the father 36, and the father was 18 when the son was born, which matches what he says.

Q: Priti is thrice as old as Prem. Seema will be twice as old as Priti, 6 years hence. Six years ago Prem was 5 (five) years old. What is Seema's present age ?

Seema's present age is 72 years.Work from Prem's age, the only fixed number:\[ \begin{aligned} \text{Prem now} &= 5 + 6 = 11 \\ \text{Priti now} &= 3 \times 11 = 33 \\ \text{Seema} + 6 &= 2 \times (33 + 6) = 78 \\ \text{Seema now} &= 72 \end{aligned} \]Both ages in the 'six years hence' statement must be taken six years on. Doubling Priti's present age, 66, and then subtracting 6 gives 60, the trap among the options.

Q: The present age of a father is three times the age of his son. After 10 years, the father's age will be twice the age of his son. The present age of the son is

The son's present age is 10 years.Let the son's age be s, so the father's is 3s. In 10 years the father will be twice the son's age:\[ \begin{aligned} 3s + 10 &= 2(s + 10) \\ 3s + 10 &= 2s + 20 \\ s &= 10 \end{aligned} \]Check: the son is 10 and the father 30; in 10 years they will be 20 and 40, and 40 is twice 20.With a son of 15 the father would be 45, and in 10 years 55 against 25, which is not double; 20 and 25 fail in the same way.

Q: The sum of ages of A and B is 60 years. If A is twice as old as B, what is B's age ?

B's age is 20 years.A is twice as old as B, so A = 2B, and together they total 60:\[ \begin{aligned} 2B + B &= 60 \\ 3B &= 60 \\ B &= 20 \end{aligned} \]So B is 20 and A is 40. Check: 40 + 20 = 60, and 40 is twice 20.With B at 15, A would be 30 and the total only 45; with 18 the total is 54, and with 25 it is 75. Only 20 gives 60.

Q: Amit is now 6 times as old as his son. Four years from now, the sum of their ages will be 43 years. Determine Amit's present age.

Amit's present age is 30 years.Let the son's age be s, so Amit is 6s. In four years both are 4 years older:\[ \begin{aligned} (6s + 4) + (s + 4) &= 43 \\ 7s + 8 &= 43 \\ s = 5, \ 6s &= 30 \end{aligned} \]Check: Amit is 30 and his son 5; in four years they will be 34 and 9, which add to 43.32, 34 and 28 are not multiples of 6, so none can be six times a whole-number age; 34 is Amit's age four years from now, a common slip.

Important Instructions

21.

Eighteen years ago, the ratio of P's age to Q's age was 8:13. Their present age ratios are 5:7. Then the present age of P is

A.50 years
B.60 years
C.70 years
D.None of these

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: A

P's present age is 50 years.

Let the present ages be \(5x\) and \(7x\). Eighteen years ago they were in the ratio 8:13.

\[ \begin{aligned} \frac{5x - 18}{7x - 18} &= \frac{8}{13} \\ 65x - 234 &= 56x - 144 \\ 9x &= 90,\ x = 10 \end{aligned} \]

So P is \(5 \times 10 = 50\) and Q is 70. Check: 18 years ago they were 32 and 52, and \(32:52 = 8:13\). 70 years is Q's age, not P's.

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22.

The ratio of the present age of father to that of son is 7:2. After 10 years their ages will be in the ratio of 9:4. The present age of father is

A.35 years
B.40 years
C.30 years
D.25 years

Exam Year(s)

Tripura Public Service Commission - 2019,

Answer: A

The father's present age is 35 years.

Let the present ages be \(7k\) and \(2k\). After 10 years:

\[ \begin{aligned} \frac{7k + 10}{2k + 10} &= \frac{9}{4} \\ 28k + 40 &= 18k + 90 \\ k &= 5 \end{aligned} \]

So the father is 35 and the son 10. Check: in 10 years they will be 45 and 20, and 45 : 20 = 9 : 4. 40, 30 and 25 are not multiples of 7, so none of them can be the father's share of a 7 : 2 ratio in whole years.

Ratio questions on ages are solved by writing the present ages as multiples of one unknown and using the fact that every age changes by the same number of years.

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23.

A father tells his son, "I was of your present age when you were born". If the father is 36 now, how old was the boy five years back ?

A.13
B.15
C.17
D.20

Exam Year(s)

Tripura Public Service Commission - 2019,

Answer: A

The boy was 13 five years ago.

The father's age when the son was born equals the son's present age, \(s\). The father is that much older than the son, so his present age is \(s + s = 2s\):

\[ \begin{aligned} 2s &= 36 \\ s &= 18 \end{aligned} \]

Five years ago the boy was \(18 - 5 = 13\). 18 would be his present age, which is not what is asked, and 15, 17 and 20 do not follow.

Check: the son is 18 and the father 36, and the father was 18 when the son was born, which matches what he says.

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24.

Priti is thrice as old as Prem. Seema will be twice as old as Priti, 6 years hence. Six years ago Prem was 5 (five) years old. What is Seema's present age ?

A.72 years
B.60 years
C.42 years
D.None of these.

Exam Year(s)

Tripura Public Service Commission - 2013,

Answer: A

Seema's present age is 72 years.

Work from Prem's age, the only fixed number:

\[ \begin{aligned} \text{Prem now} &= 5 + 6 = 11 \\ \text{Priti now} &= 3 \times 11 = 33 \\ \text{Seema} + 6 &= 2 \times (33 + 6) = 78 \\ \text{Seema now} &= 72 \end{aligned} \]

Both ages in the 'six years hence' statement must be taken six years on. Doubling Priti's present age, 66, and then subtracting 6 gives 60, the trap among the options.

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25.

The present age of a father is three times the age of his son. After 10 years, the father's age will be twice the age of his son. The present age of the son is

A.10 years
B.15 years
C.20 years
D.25 years

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: A

The son's present age is 10 years.

Let the son's age be s, so the father's is 3s. In 10 years the father will be twice the son's age:

\[ \begin{aligned} 3s + 10 &= 2(s + 10) \\ 3s + 10 &= 2s + 20 \\ s &= 10 \end{aligned} \]

Check: the son is 10 and the father 30; in 10 years they will be 20 and 40, and 40 is twice 20.

With a son of 15 the father would be 45, and in 10 years 55 against 25, which is not double; 20 and 25 fail in the same way.

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26.

The sum of ages of A and B is 60 years. If A is twice as old as B, what is B's age ?

A.15 years
B.18 years
C.20 years
D.25 years

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: C

B's age is 20 years.

A is twice as old as B, so A = 2B, and together they total 60:

\[ \begin{aligned} 2B + B &= 60 \\ 3B &= 60 \\ B &= 20 \end{aligned} \]

So B is 20 and A is 40. Check: 40 + 20 = 60, and 40 is twice 20.

With B at 15, A would be 30 and the total only 45; with 18 the total is 54, and with 25 it is 75. Only 20 gives 60.

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27.

Amit is now 6 times as old as his son. Four years from now, the sum of their ages will be 43 years. Determine Amit's present age.

A.30 years
B.32 years
C.34 years
D.28 years

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: A

Amit's present age is 30 years.

Let the son's age be s, so Amit is 6s. In four years both are 4 years older:

\[ \begin{aligned} (6s + 4) + (s + 4) &= 43 \\ 7s + 8 &= 43 \\ s = 5, \ 6s &= 30 \end{aligned} \]

Check: Amit is 30 and his son 5; in four years they will be 34 and 9, which add to 43.

32, 34 and 28 are not multiples of 6, so none can be six times a whole-number age; 34 is Amit's age four years from now, a common slip.

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28.

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

A.6
B.8
C.9
D.10
E.11

Answer: D

Let C's age be \(x\) years. Then, B's age = \(2x\) years. A's age \(=(2x+2)\) years.

\(\therefore (2x + 2) + 2x + x = 27\)

\(\Rightarrow 5x = 25\)

\(\Rightarrow x=5\)

Hence, B's age \(=2x=10\) years.

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29.

Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ?

A.20 years
B.25 years
C.30 years
D.35 years

Answer: B

Let varun's age = \(x\) years.

From the given conditions,

\(\Rightarrow x+1 = 2(x-12)\)

\(\Rightarrow x=25\) years.

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30.

Rajan's present age is three times his daughter's and nine-thirteenth of his mother's present age. The sum of the present ages of all three of them is 125 years. What is the difference between the present ages of Rajan's daughter and Rajan's mother ?

A.30 years
B.40 years
C.50 years
D.60 years

Answer: C

Let Rajan's present age be '\(x \)' years.

Then his daughter's present age is = \(\frac{x}{3}\) years.

His mother's present age = \(\frac{13x}{9}\) years.

Now, according to the question,
\(\therefore x+\frac{x}{3}+\frac{13x}{9}=125\)

\(\Rightarrow x=\)\(\frac{125*9}{25}\)\(=45\)

Therefore, required difference = \(\frac{13x}{9}-\)\(\frac{x}{3}=13x -\)\(\frac{3x}{9}=\)\(\frac{10x}{9}\)

\(\Rightarrow \frac{10*45}{9}\)= 50 years

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