Question

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. What are their current ages?

• A. 36, 9
• B. 34, 11
• C. 32, 13
• D. 30, 15

Hint:

Solve age problems by setting up equations for current and past conditions, and test options for quick verification.

Answer 1

The Correct Option is A

Let father’s age = \( F \), son’s age = \( S \). 
Given: \( F + S = 45 \), and five years ago: \( (F - 5)(S - 5) = 124 \). 
From \( F + S = 45 \), \( F = 45 - S \). Substitute into the second equation: 
\[ (45 - S - 5)(S - 5) = 124 \Rightarrow (40 - S)(S - 5) = 124 \] \[ 40S - 5S^2 - 200 + 5S = 124 \Rightarrow -5S^2 + 45S - 200 = 124 \] \[ -5S^2 + 45S - 324 = 0 \Rightarrow 5S^2 - 45S + 324 = 0 \Rightarrow S^2 - 9S + 64.8 = 0 \] Discriminant: \( 81 - 4 \times 64.8 \approx 81 - 259.2<0 \). 
Recalculate correctly: 
Test options: \( F = 36, S = 9 \): \( 36 + 9 = 45 \), and \( (36 - 5)(9 - 5) = 31 \times 4 = 124 \). 
Thus, the answer is 36, 9.