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### Question 1

The ratio of present ages of two monuments A and B is $4{1/5}$. After 4 years later the age of A will be 109 years. What is the present age of B?

**A**

25 years.

**B**

20 years.

**C**

15 years.

**D**

30 years.

**Soln.**

**Ans: a**

The ratio of ages of A and B is given as ${21/5}$, which is same as: $4{1/5}$. So we can write the present ages of A and B, respectively, as 21r and 5r years. 4 years later the age of A is $21r + 4 = 109$ which gives r = 5. The age of B, therefore, is 5r = 5 × 5 = 25 years.

### Question 2

My father was 31 years old when I was born. My mother's age was 18 when my sister, who is 6 years younger to me, was born. What is the difference between the ages of my parents?

**A**

19 years.

**B**

20 years.

**C**

18 years.

**D**

21 years.

**Soln.**

**Ans: a**

If the age of my father is F, then my age is F - 31, so my younger sister's age is (F - 31) - 6, which is = F - 37. If my mother's age is M, then M = (my sister's age) + 18, i.e., M = (F - 37) + 18. We get F - M = 19 years.

This question can be solved directly also. The age of my father at the time of birth of my sister was 31 + 6 = 37. At the time my mother was 18 years. So the difference between their ages = 37 - 18 = 19 years.

### Question 3

The square root of twice my present age is equal to the sum of the square roots of my ages 7 years back and 7 years hence. What is my present age?

**A**

7 years.

**B**

8 years.

**C**

6 years.

**D**

14 years.

**Soln.**

**Ans: a**

Let the present age be x. Then $√(x - 7) + √(x + 7)$ = $√{2x}$. Squaring both sides, $(√(x - 7))^2 + (√(x + 7))^2 + 2√{x^2 - 7^2}$ = $2x$ which gives $x - 7 + x + 7 + 2√{x^2 - 7^2}$ = $2x$. Cancelling, and simplifying, $2√(x^2 - 49) = 0$, which leads to x = 7 years.

### Question 4

The ages of two friends are in the ratio 2:17. What is the age of the younger friend if the sum of their ages is 38 years?

### Question 5

The sum of reciprocals of my ages 8 years back and 8 years later is ${70/1161}$. What is my present age?

**A**

35 years.

**B**

36 years.

**C**

34 years.

**D**

37 years.

**Soln.**

**Ans: a**

Let the present age be x. Then $1/{x + 8} + 1/{x - 8}$ = ${70/1161}$. At this stage a better option is that you try putting the given answers into this expression one by one. The other option is to simplify this expression into a quadratic equation ${2x}/{x^2 - 64}$ = ${70/1161}$. This can now be solved to give x = 35 years.

This Blog Post/Article "Problems on Ages Quiz Set 006" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2017-10-26.