UPSC Prelims 2015 CSAT Paper II · Q16 of 74 Basic Numeracy easy

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 ?

  1. (a) 7 years
  2. (b) 5 years
  3. (c) 4 years
  4. (d) 3 years ✓ UPSC's answer

Why the answer is (d)

• Let the son's age be represented by the variable 'x'.

• The father's age is given as nine times the son's age, which is 9x.

• The mother's age is given as eight times the son's age, which is 8x.

• The sum of the father's and mother's ages is stated to be 51 years, leading to the equation 9x + 8x = 51.

• Combining like terms gives 17x = 51.

• Solving for x by dividing 51 by 17 results in x = 3, which is the son's age.

Why the other options are wrong

(a) 7 years
If the son were 7, the sum of the parents' ages would be 119, not 51.
(b) 5 years
If the son were 5, the sum of the parents' ages would be 85, not 51.
(c) 4 years
If the son were 4, the sum of the parents' ages would be 68, not 51.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

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