Question

The age of father 5 years ago was thrice the age of his son. 25 years hence, the age of son will be 3 / 4^th of his father’s age. Find sum of their present age
1. 40 years
2. 50 years
3. 34 years
4. None

Answer 1

Correct Answer - Option 3 : 34 years

Given:

5 years ago, ratio of ages of father and son = 3 ∶ 1

25 years hence, ratio of their ages = 4 ∶ 3

Concept used:

To convert any ratio to exact value, we should have to multiply any constant value

Let, ages of father and son 5 years ago was = 3x and x respectively

∴ 25 years hence, age of father = 3x + 5 + 25 = (3x + 30) years and age of son = x + 5 + 25 = (x + 30) years

⇒ (3x + 30) / (x + 30) = 4 / 3

⇒ (x + 10) / (x + 30) = 4 / 9

⇒ 9x + 90 = 4x + 120

⇒ 5x = 30

∴ x = 6

∴ father’s age, 5 years ago = 18 years and son’s age = 6 years

Therefore, Sum of their present ages = (18 + 6) + (5 + 5) = 24 + 10 = 34 years