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GATE 2024 EC – Question 3

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

Five years ago, the ratio of Aman’s age to his father’s age was 1:4, and five years from now, the ratio will be 2:5. What was his father’s age when Aman was born?

  1. 28 years
  2. 30 years
  3. 35 years
  4. 32 years

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Show answer and explanation

Correct answer: (B) 30 years

Explanation

Let Aman be $a$ and his father $f$ now. $\frac{a-5}{f-5}=\frac14$ gives $f=4a-15$. $\frac{a+5}{f+5}=\frac25$ gives $5a+25=2f+10$. Substituting, $5a+25=8a-30+10$, so $a=15$ and $f=45$. When Aman was born his father was $45-15=30$ years old.