# Problems on Ages Quiz Set 004

### Question 1

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 2

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.

### Question 3

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 4

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 5

The ratio of present ages of two monuments A and B is \$5{1/5}\$. If the difference of their ages is 105, then what is the age of B?

A

25 years.

B

20 years.

C

15 years.

D

30 years.

Soln.
Ans: a

The ratio of ages of A and B is given as \${26/5}\$, which is same as: \$5{1/5}\$. So we can write the present ages of A and B, respectively, as 26r and 5r years. The difference is \$26r - 5r = 105\$ which gives r = 5. The age of B, therefore, is 5r = 5 × 5 = 25 years.