UPSC Prelims 2015·CSAT·Quantitative Aptitude·Arithmetic

A father is nine times as old as his son and the mother is eight times as old as the son. The sum of the father's and the mother's age is 51 years. What is the age of the son?

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Last updated 23 May 2026, 3:31 pm IST
  1. A7 year
  2. B5 year
  3. C4 year
  4. D3 yearCorrect

Explanation

Let the son's age be S. From the problem statement: 1. Father's age (F) = 9 * Son's age (S) = 9S 2. Mother's age (M) = 8 * Son's age (S) = 8S 3. The sum of the father's and mother's age is 51 years: F + M = 51 Substitute the expressions for F and M from points 1 and 2 into point 3: 9S + 8S = 51 17S = 51 S = 51 / 17 S = 3 So, the son's age is 3 years. Analysis of options: A) 7 year: If S=7, F=63, M=56. F+M = 119, not 51. B) 5 year: If S=5, F=45, M=40. F+M = 85, not 51. C) 4 year: If S=4, F=36, M=32. F+M = 68, not 51. D) 3 year: If S=3, F=27, M=24. F+M = 27+24 = 51. This matches the given condition. Therefore, option D is correct.
Quantitative Aptitude: A father is nine times as old as his son and the mother is eight times as old as the son. The sum of the father's and th

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