# Problems on Ages Quiz Set 018

### Question 1

The sum of the ages of 10 calves of a whale born at a gap of 4 years is 280. What is the age of the youngest calf?

A

10 years.

B

11 years.

C

9 years.

D

12 years.

Soln.
Ans: a

The ages of the calves are in an AP with d = 4, n = 10, and sum S = 280. We have to find the first term a. We know S = \${n/2} × (2a + (n-1)d)\$ Putting the values 280 = \${10/2} × (2a + (10-1)×4)\$. Solving, get a = 10 years.

### Question 2

The ages of three friends are in the ratio 2:23:3. What is the age of the youngest friend if the sum of their ages 3 years back was 159 years?

A

12 years.

B

13 years.

C

11 years.

D

14 years.

Soln.
Ans: a

Let the ages of three friends be 2r, 23r and 3r. The youngest of these is 2r. We have been given their sum 3 years back. So (2 + 23 + 3)r - (3 × 3) = 159. Solving, we get r = 6. The youngest is 2 × 6 = 12 years.

### Question 3

The ratio of present ages of two monuments A and B is \$2{9/10}\$. After 4 years later the age of A will be 381 years. What is the present age of B?

A

130 years.

B

120 years.

C

110 years.

D

140 years.

Soln.
Ans: a

The ratio of ages of A and B is given as \${29/10}\$, which is same as: \$2{9/10}\$. So we can write the present ages of A and B, respectively, as 29r and 10r years. 4 years later the age of A is \$29r + 4 = 381\$ which gives r = 13. The age of B, therefore, is 10r = 10 × 13 = 130 years.

### Question 4

The ratio of present ages of two monuments A and B is \$2{1/4}\$. After 3 years later the age of A will be 102 years. What is the present age of B?

A

44 years.

B

40 years.

C

36 years.

D

48 years.

Soln.
Ans: a

The ratio of ages of A and B is given as \${9/4}\$, which is same as: \$2{1/4}\$. So we can write the present ages of A and B, respectively, as 9r and 4r years. 3 years later the age of A is \$9r + 3 = 102\$ which gives r = 11. The age of B, therefore, is 4r = 4 × 11 = 44 years.

### Question 5

After 5 years from today the ages of three friends will be in an AP(arithmetic progression), and their sum would be 99. What is the age of the middle friend today?

A

28 years.

B

29 years.

C

27 years.

D

30 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 = 99. We get a = 99/3 = 33. So, the age of the middle friend today is a - 5 = 28 years. 