Question

If the sum of the ages of a father and his son is 65 years and twice the difference of their ages is 50 years, then the age of the father in years is

• A. 45
• B. 40
• C. 50
• D. 55

Answer 1

The Correct Option is A

Let the age of the father be \( f \) and the age of the son be \( s \). We are given the following two conditions: 1. The sum of their ages is 65 years: \[ f + s = 65 \] 2. Twice the difference of their ages is 50 years: \[ 2(f - s) = 50 \] Simplify the second equation: \[ f - s = 25 \] Now, we have the system of equations: 1. \( f + s = 65 \) 2. \( f - s = 25 \) To solve this system, add the two equations: \[ (f + s) + (f - s) = 65 + 25 \] \[ 2f = 90 \] \[ f = 45 \] Thus, the age of the father is 45 years.

The correct option is (A): \(45\)