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.