A father said to his son, "n years back I was as old as you are now. My present age is four times your age n years back". If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages?
- (a) 30 years ✓ UPSC's answer
- (b) 32 years
- (c) 34 years
- (d) 36 years
Why the answer is (a)
• Let the son be S and the father F years old now.
• "n years back I was as old as you are now": F − n = S, so n = F − S.
• "My present age is four times your age n years back": F = 4(S − n) = 4(S − F + S) = 4(2S − F), so 5F = 8S.
• With F + S = 130: S = 50 and F = 80. The difference is 30 years — option (a).
Why the other options are wrong
- (b) 32 years
- The calculated difference is 30 years, not 32 years.
- (c) 34 years
- The calculated difference is 30 years, not 34 years.
- (d) 36 years
- The calculated difference is 30 years, not 36 years.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.