Father–Son — “A father is currently 3 times as old as his son. Eight years ago, the father was 5 times the son. What is the son’s present age?”

Introduction / Context:Two multiplicative relationships at different times determine two linear equations. Solving them yields the son’s present age uniquely; the method is standard for age word problems.

Given Data / Assumptions:

• Let son now = s; father now = 3s.
• Eight years ago: father 3s − 8; son s − 8.
• Given: 3s − 8 = 5(s − 8).

Concept / Approach:Substitute the expressions for “8 years ago” into the equation and solve for s. Check quickly against both relations for consistency.

Step-by-Step Solution:

Verification / Alternative check:Now father = 48. Eight years ago: father 40; son 8 ⇒ indeed 40 = 5 × 8. Presently father 48 = 3 × 16 as required.

Why Other Options Are Wrong:12/14/20/10 fail either the “3 times now” or the “5 times 8 years ago” constraints when checked.

Common Pitfalls:Dropping the “−8” on only one person; mixing up 3s with 5s − 40; or solving but forgetting to answer the son’s present age.

Final Answer:16 years