# Problems on Ages Quiz Set 003

### Question 1

The ages of two friends are 4 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

8 years.

B

9 years.

C

7 years.

D

10 years.

Soln.
Ans: a

If the age of the third friend is x. Then for a GP, x = \$√(4 × 16)\$ = 8 years.

### Question 2

5 years back the ratio of ages of X and Y was \${35/43}\$. The ratio of their ages 3 years from now would be \${43/51}\$. What is the present age of X?

A

40 years.

B

41 years.

C

39 years.

D

42 years.

Soln.
Ans: a

Let their present ages be x and y. Then \${x - 5}/{y - 5} = \$ \${35/43}\$. Similarly, \${x + 3}/{y + 3} = \$ \${43/51}\$. Solving these equations for x and y, we get y = 48, and x = 40 years as the answer.

### Question 3

My father was 25 years old when I was born. My mother's age was 23 when my sister, who is 2 years younger to me, was born. What is the difference between the ages of my parents?

A

4 years.

B

5 years.

C

3 years.

D

6 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) - 2, which is = F - 27. If my mother's age is M, then M = (my sister's age) + 23, i.e., M = (F - 27) + 23. We get F - M = 4 years.

This question can be solved directly also. The age of my father at the time of birth of my sister was 25 + 2 = 27. At the time my mother was 23 years. So the difference between their ages = 27 - 23 = 4 years.

### Question 4

The age of father tortoise is 10 times the age of his son. After 12 years his age will be 6 times the age of his son. What would be the ratio of their ages 120 years from today?

A

2.

B

5.

C

3.

D

4.

Soln.
Ans: a

If the age of the son today is s, the age of the father is 10s. After 12 years, we have 10s + 12 = 6(s + 12). Solving for s, we get s = 15 years. The ratio of their ages after 120 years = \${10s + 120}/{s + 120}\$. Substituting s and simplifying we get the ratio as 2.

### Question 5

The age of father tortoise is 14 times the age of his son. After 40 years his age will be 6 times the age of his son. What would be the ratio of their ages 300 years from today?

A

2.

B

5.

C

3.

D

4.

Soln.
Ans: a

If the age of the son today is s, the age of the father is 14s. After 40 years, we have 14s + 40 = 6(s + 40). Solving for s, we get s = 25 years. The ratio of their ages after 300 years = \${14s + 300}/{s + 300}\$. Substituting s and simplifying we get the ratio as 2. 