Five years ago, a father’s age was 5 times his son’s age. Today, the father’s age is 3 times his son’s age. What is the father’s present age?

Difficulty: Easy

33 years
30 years
45 years
None of these
35 years

Correct Answer: 30 years

Explanation:

Introduction:
Age problems translate to linear equations with time shifts. We express both ages at two moments and solve for the present ages that satisfy both relationships.

Given Data / Assumptions:

Let current ages be F (father) and S (son).
Five years ago: F − 5 = 5(S − 5).
Now: F = 3S.

Concept / Approach:
Substitute F = 3S into the first equation, then solve for S. Finally obtain F and select the correct option.

Step-by-Step Solution:

F − 5 = 5(S − 5) → F − 5 = 5S − 25 → F = 5S − 20.But F = 3S → 3S = 5S − 20 → 2S = 20 → S = 10.Then F = 3S = 30.

Verification / Alternative check:
Five years ago: father 25, son 5 → indeed 25 = 5*5; now 30 = 3*10, both conditions satisfied.

Why Other Options Are Wrong:
33, 35, 45 do not satisfy both time-based relationships simultaneously.

Common Pitfalls:
Misapplying the time shift to only one person or mixing the 5-year difference incorrectly.

Five years ago, a father’s age was 5 times his son’s age. Today, the father’s age is 3 times his son’s age. What is the father’s present age?

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