# Problems on Ages Quiz Set 002

### Question 1

When the daughter was born, the age of her mother was same as the daughter's age today. What was the age of the daughter 5 years back, if the age of the mother today is 44 years?

A

17 years.

B

18 years.

C

16 years.

D

19 years.

Soln.
Ans: a

Clearly, the age of the mother is twice her daughter's present age. So the daughter's age today is 44/2 = 22 years. And, 5 years back the age of the daughter was 22 - 5 = 17 years.

### Question 2

The ages of three friends are in the ratio 13:11:2. What is the age of the youngest friend if the sum of their ages is 52 years?

A

4 years.

B

5 years.

C

3 years.

D

6 years.

Soln.
Ans: a

Let the ages of three friends be 13r, 11r and 2r. The youngest of these is 2r. We have been given their sum. So (13 + 11 + 2)r = 52. Solving, we get r = 2. The youngest is 2 × 2 = 4 years.

### Question 3

The square root of twice my present age is equal to the sum of the square roots of my ages 8 years back and 8 years hence. What is my present age?

A

8 years.

B

9 years.

C

7 years.

D

16 years.

Soln.
Ans: a

Let the present age be x. Then \$√(x - 8) + √(x + 8)\$ = \$√{2x}\$. Squaring both sides, \$(√(x - 8))^2 + (√(x + 8))^2 + 2√{x^2 - 8^2}\$ = \$2x\$ which gives \$x - 8 + x + 8 + 2√{x^2 - 8^2}\$ = \$2x\$. Cancelling, and simplifying, \$2√(x^2 - 64) = 0\$, which leads to x = 8 years.

### Question 4

After 5 years from today the ages of three friends will be in an AP(arithmetic progression), and their sum would be 45. What is the age of the middle friend today?

A

10 years.

B

11 years.

C

9 years.

D

12 years.

Soln.
Ans: a

Let the ages after 5 years be a - d, a and a + d. The sum is given to us. So (a - d) + a + (a + d) = 3a = 45. We get a = 45/3 = 15. So, the age of the middle friend today is a - 5 = 10 years.

### Question 5

The ages of two friends are 9 and 16 years respectively. They are looking for a special third friend whose age is in-between their ages. What should be the age of the third friend if the ages of all three have to be in a GP(geometric progression)?

A

12 years.

B

13 years.

C

11 years.

D

14 years.

Soln.
Ans: a

If the age of the third friend is x. Then for a GP, x = \$√(9 × 16)\$ = 12 years. 