Question

The twice of the difference of ages of father and son is 60 years. 5 years hence, father’s age will be 15 years more than 1½ times of ages of his son, Find the age of father.
1. 55 years
2. 60 years
3. 52 years
4. 65 years

Answer 1

Correct Answer - Option 1 : 55 years

Given:

2 (Father’s age – son’s age) = 60 years

(Father’s age + 5 years) – 15 = 3 / 2 × (son’s age + 5 years)

Let, present ages of father and son be x and y respectively.

∴ 2 (x – y) = 60

∴ x – y = 30     ---- (1)

5 years hence, age of father = (x + 5) years and son’s age = (y + 5) years

∴ (x + 5) – 15 = 3 / 2 × (y + 5)

⇒ 2 (x – 10) = 3 (y + 5)

⇒ 2x – 20 = 3y + 15

⇒ 2x – 3y = 35     ---- (2)

On using eqn. (1) and (2)

⇒ y = 25 and x = 55

Therefore, age of father = 55 years