Question

There are three people in a family, husband, wife, and their son. The husband's age is four times his son's age and the wife is 9 years younger than her husband. What is the ratio of the ages of husband, wife, and son if the sum of their ages is 99 years?
1. 20 : 16 : 5
2. 12 : 9 : 3
3. 16 : 13 : 4
4. 16 : 11 : 4
5. None of these

Answer 1

Correct Answer - Option 3 : 16 : 13 : 4

Given:

Husband's age = 4 × son's age 

Wife's age = husband's age - 9

Sum of ages = 99 years

Calculation:

Let husband's age be 4x.

∴ Son's age = x, wife's age = 4x - 9

A.T.Q

4x + x + 4x -9 = 99 years

⇒ 9x = 108

⇒ x = 12 years

Husband's age = 12 × 4 = 48 years

Wife's age = 48 - 9 = 39 years

Required ratio = 48 : 39 : 12 = 16 : 13 : 4

∴ The ratio is 16 : 13 : 4