# Problems on Ages Quiz Set 001

### Question 1

The square root of twice my present age is equal to the sum of the square roots of my ages 10 years back and 10 years hence. What is my present age?

A

10 years.

B

11 years.

C

9 years.

D

20 years.

Soln.
Ans: a

Let the present age be x. Then \$√(x - 10) + √(x + 10)\$ = \$√{2x}\$. Squaring both sides, \$(√(x - 10))^2 + (√(x + 10))^2 + 2√{x^2 - 10^2}\$ = \$2x\$ which gives \$x - 10 + x + 10 + 2√{x^2 - 10^2}\$ = \$2x\$. Cancelling, and simplifying, \$2√(x^2 - 100) = 0\$, which leads to x = 10 years.

### Question 2

The ages of two friends are in the ratio 13:7. What is the age of the younger friend if the sum of their ages is 100 years?

A

35 years.

B

36 years.

C

34 years.

D

37 years.

Soln.
Ans: a

Let the ages be 13r and 7r. The younger is 7r. We have been given their sum. So (13 + 7)r = 100. Solving, we get r = 5. The younger is 7 × 5 = 35 years.

### Question 3

The sum of the ages of 10 calves of a whale born at a gap of 6 years is 390. What is the age of the youngest calf?

A

12 years.

B

13 years.

C

11 years.

D

14 years.

Soln.
Ans: a

The ages of the calves are in an AP with d = 6, n = 10, and sum S = 390. We have to find the first term a. We know S = \${n/2} × (2a + (n-1)d)\$ Putting the values 390 = \${10/2} × (2a + (10-1)×6)\$. Solving, get a = 12 years.

### Question 4

The ratio of present ages of two monuments A and B is \$1{9/11}\$. If the difference of their ages is 117, then what is the age of B?

A

143 years.

B

132 years.

C

121 years.

D

154 years.

Soln.
Ans: a

The ratio of ages of A and B is given as \${20/11}\$, which is same as: \$1{9/11}\$. So we can write the present ages of A and B, respectively, as 20r and 11r years. The difference is \$20r - 11r = 117\$ which gives r = 13. The age of B, therefore, is 11r = 11 × 13 = 143 years.

### Question 5

My father was 25 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

13 years.

B

14 years.

C

12 years.

D

15 years.

Soln.
Ans: a

If the age of my father is F, then my age is F - 25, so my younger sister's age is (F - 25) - 6, which is = F - 31. If my mother's age is M, then M = (my sister's age) + 18, i.e., M = (F - 31) + 18. We get F - M = 13 years.

This question can be solved directly also. The age of my father at the time of birth of my sister was 25 + 6 = 31. At the time my mother was 18 years. So the difference between their ages = 31 - 18 = 13 years.