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?

• A. 3 : 8
• B. 1 : 3
• C. 2 : 7
• D. 2 : 5

Answer 1

Answer:

B. 1 : 3

Solution: 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.