Question

The sum of the presents age of a father and son is 52 years Four years hence, the son's age will be 1/4 that of the father. What will be the ratio of the age of the son and father, 10 years from now?
1. 3 : 8
2. 1 : 3
3. 2 : 7
4. 2 : 5

Answer 1

Correct Answer - Option 2 : 1 : 3

Given:

Father’s present age + Son’s present age = 52 years

Son’s age after 4 years = 1/4 × Father’s age after 4 years

Concept used:

Using the concept of the linear equation.

Calculation:

Let the present age of the son be x years.

And the present age of the father is (52 – x) years.

According to the question,

Son’s age after 4 years = 1/4 × Father’s age after 4 years

⇒ (x + 4) = 1/4 × (52 – x + 4)

⇒ (x + 4) × 4 = 56 – x

⇒ 4x + 16 = 56 – x

⇒ 5x = 40

⇒ x = 8 years

Son’s present age = 8 years

Father’s present age = 52 – 8

⇒ Father’s present age = 44 years

Required ratio = (Age of son after 10 years)/(Age of father after 10 years)

⇒ Required ratio = (8 + 10)/(44 + 10)

⇒ Required ratio = 18/54

⇒ Required ratio = 1/3

∴ The ratio of the age of the son and father, 10 years from now is 1 ∶ 3.