UPSC Prelims 2015 · CSAT
Question 50: Basic Numeracy
A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair. While preparing the bill, the bill clerk interchanged the number of black and brown pairs by mistake which increased the bill by 100%. What was the number of pairs of brown socks in the original order ?
AnswerUPSC’s answer is (d).
Let a brown pair cost p, so a black pair costs 3p. Original bill = 5 × 3p + n × p = 15p + np for n brown pairs. After the swap the clerk bills n black pairs and 5 brown pairs: 3np + 5p. That is double the original: 3np + 5p = 2(15p + np), so 3n + 5 = 30 + 2n, giving n = 25. Check: original 40p, new 80p.
Why each option is right or wrong
- (a) Wrong: n = 10 gives bills of 25p and 35p, not a doubling.
- (b) Wrong: n = 15 gives bills of 30p and 50p, not a doubling.
- (c) Wrong: n = 20 gives bills of 35p and 65p, not a doubling.
- (d) Right: n = 25 gives 40p and 80p.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2015, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.