# Problems on Ages Quiz Set 019

### Question 1

Each year the ages of three friends are in an AP(arithmetic progression). The age of middle friend today is 27 years. What would be the sum of their ages 10 years from now?

A

111 years.

B

112 years.

C

110 years.

D

113 years.

Soln.
Ans: a

Let the present ages of the three friends be a - d, a and a + d. As of today a = 27. Ten years later their ages would be a + 10 - d, a + 10, a + 10 + d. Adding these we get 3a + 30 which equals 3 × 27 + 30 = 111 years.

### Question 2

The ages of three friends are in the ratio 7:17:19. What is the age of the youngest friend if the sum of their ages 4 years back was 74 years?

A

14 years.

B

15 years.

C

13 years.

D

16 years.

Soln.
Ans: a

Let the ages of three friends be 7r, 17r and 19r. The youngest of these is 7r. We have been given their sum 4 years back. So (7 + 17 + 19)r - (3 × 4) = 74. Solving, we get r = 2. The youngest is 7 × 2 = 14 years.

### Question 3

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 14 years back, if the age of the mother today is 44 years?

A

8 years.

B

9 years.

C

7 years.

D

10 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, 14 years back the age of the daughter was 22 - 14 = 8 years.

### Question 4

My father was 32 years old when I was born. My mother's age was 32 when my sister, who is 6 years younger to me, was born. What is the difference between the ages of my parents?

A

6 years.

B

7 years.

C

5 years.

D

8 years.

Soln.
Ans: a

If the age of my father is F, then my age is F - 32, so my younger sister's age is (F - 32) - 6, which is = F - 38. If my mother's age is M, then M = (my sister's age) + 32, i.e., M = (F - 38) + 32. We get F - M = 6 years.

This question can be solved directly also. The age of my father at the time of birth of my sister was 32 + 6 = 38. At the time my mother was 32 years. So the difference between their ages = 38 - 32 = 6 years.

### Question 5

The age of father tortoise is 12 times the age of his son. After 30 years his age will be 6 times the age of his son. What would be the ratio of their ages 250 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 12s. After 30 years, we have 12s + 30 = 6(s + 30). Solving for s, we get s = 25 years. The ratio of their ages after 250 years = \${12s + 250}/{s + 250}\$. Substituting s and simplifying we get the ratio as 2. 