The sum of the present ages of a father and son is 52 years. Four years hence, the son's age will be ¼ that of the father. What will be the ratio of the ages of the son and father, 10 years from now?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 1 : 3.
Let the present age of the son be x years
The present age of the father is (52 – x) years
According to the question,
Age of son after 4 years = 1/4 × Age of father after four years
⇒ (x + 4) = 1/4 × (52 – x + 4)
⇒ (x + 4) × 4 = 56 – x
⇒ 4x + 16 = 56 – x
⇒ 5x = 40
⇒ x = 8 years
The present age of son = 8 years
The present age of father = 52 – 8 = 44 years
Age of son after 10 years = 8 + 10 = 18 years
Age of father after 10 years = 44 + 10 = 54 years
Ratio of their ages = 18 : 54 = 1 : 3