# Problems on Ages Quiz Set 006

### 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?

A

4 years.

B

5 years.

C

3 years.

D

6 years.

Soln.
Ans: a

Let the ages be 2r and 17r. The younger is 2r. We have been given their sum. So (2 + 17)r = 38. Solving, we get r = 2. The younger is 2 × 2 = 4 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. 