Question

A father is 4 times his son’s age and in 30 years son’s age will be half of his father’s age. How old are the father and son now?

• A. 60, 30
• B. 90, 45
• C. 60, 45
• D. 60, 15

Hint:

Always define the variable for the smaller age (son), and relate other ages based on the problem.

Answer 1

The Correct Option is D

Step 1: Let son's age be \( x \), then father's age = \( 4x \)
Step 2: In 30 years
Father’s age = \( 4x + 30 \), Son’s age = \( x + 30 \)
Given: Son’s age will be half of father’s age: \[ x + 30 = \frac{1}{2}(4x + 30) \] Multiply both sides by 2: \[ 2x + 60 = 4x + 30 \] \[ 60 - 30 = 4x - 2x \Rightarrow 30 = 2x \Rightarrow x = 15 \] So, son's age = 15, father's age = \( 4 \times 15 = 60 \)