2024 CSAT, all questions
UPSC Prelims 2024 · CSAT
Question 29: Basic Numeracy
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?
a30 years
b32 years
c34 years
d36 years
AnswerUPSC’s answer is (a).
Let the father's age be F and the son's S. n years back, the father's age F − n equals S. Also F = 4(S − n). So S + n = 4S − 4n, giving 3S = 5n. Then S = 5n/3 and F = S + n = 8n/3. The sum 13n/3 = 130 gives n = 30, S = 50 and F = 80. The difference is 30 years.
Why each option is right or wrong
- (a) Right. Father 80, son 50: 30 years back the father was 50 and the son was 20; 4 × 20 = 80.
- (b) Wrong. A 32-year gap does not satisfy both the relation and the sum of 130.
- (c) Wrong. A 34-year gap does not fit the conditions.
- (d) Wrong. A 36-year gap does not fit the conditions.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.