Ravi’s life stages: he spent 1/4 of his life as a boy, 1/5 as a youth, 1/3 as a man, and 13 years in old age. What is his present age?
Aptitude
Linear Equation
Difficulty: Easy
Choose an option
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A70 years
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B80 years
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C60 years
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D36 years
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E66 years
Answer
Correct Answer: 60 years
Explanation
Introduction: The life-stage breakdown forms a fractional equation in the total age. The fixed 13-year old-age segment plus fractional parts of the same total must equal the entire lifespan.
Given Data / Assumptions:
- Total age = x years.
- As a boy: x/4; as a youth: x/5; as a man: x/3; old age: 13 years.
- Sum equals x.
Concept / Approach: Add the fractions and 13, set equal to x, then solve for x using a common denominator to combine fractions exactly.
Step-by-Step Solution:
x/4 + x/5 + x/3 + 13 = x.Common denominator 60: (15x + 12x + 20x)/60 + 13 = x → 47x/60 + 13 = x.x − 47x/60 = 13 → (13x/60) = 13 → x = 60.Verification / Alternative check: Check segments: 15, 12, and 20 years sum to 47 years; plus 13 equals 60, consistent.
Why Other Options Are Wrong: 70, 80, 36, 66 do not satisfy the fractional partition equation.
Common Pitfalls: Arithmetic errors with fraction addition; ensure exact common denominator.
Final Answer: 60 years