Parent–child present multiple with past multiple: A father’s present age is three times his son’s age. Five years ago, the father’s age was four times the son’s age. What is the son’s current age?

Introduction / Context:When present and past multiplicative relationships are given, set present ages with a variable, shift by the time span, and enforce the earlier multiple to solve for that variable.

Given Data / Assumptions:

• Father now = 3s; Son now = s.
• Five years ago: (3s − 5) = 4(s − 5).

Concept / Approach:Rearrange the past-time equation to isolate s.

Step-by-Step Solution:1) 3s − 5 = 4s − 20.2) 15 = s.3) Therefore, the son’s present age is 15 years.

Verification / Alternative check:Five years ago: father = 40, son = 10 → indeed 40 = 4 × 10; now father = 45, son = 15 (3 × 15).

Why Other Options Are Wrong:

• 20/18/12/10 do not satisfy both the present triple and the past quadruple relationship simultaneously.

Common Pitfalls:Forgetting to subtract 5 from each age, or assuming both multiples hold at the same time, results in contradictions.

Final Answer:15 years