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?
Aptitude
Linear Equation
Difficulty: Easy
Choose an option
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A33 years
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B30 years
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C45 years
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DNone of these
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E35 years
Answer
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.
Final Answer: 30 years