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 ?
- (a) 10
- (b) 15
- (c) 20
- (d) 25 ✓ UPSC's answer
Why the answer is (d)
• Let a brown pair cost p, so a black pair costs 3p, and let n brown pairs be ordered.
• Correct bill = 5 × 3p + n × p = (15 + n)p.
• With the numbers swapped, the bill = n × 3p + 5 × p = (3n + 5)p.
• A 100% increase means the wrong bill is double: 3n + 5 = 2(15 + n), so n = 25.
• Hence option (d).
Why the other options are wrong
- (a) 10
- With 10 brown pairs the bill goes from 25p to 35p, a 40% rise.
- (b) 15
- With 15 brown pairs the bill goes from 30p to 50p, about a 67% rise.
- (c) 20
- With 20 brown pairs the bill goes from 35p to 65p, about an 86% rise.
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.