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 the price of a brown pair be $x$ and the price of a black pair be $3x$.
• Let the number of brown pairs ordered be $n$; the original bill amount is $5(3x) + n(x) = 15x + nx$.
• The clerk interchanged the quantities, so the billed amount became $n(3x) + 5(x) = 3nx + 5x$.
• The problem states the bill increased by 100%, meaning the new bill is double the original: $3nx + 5x = 2(15x + nx)$.
• Simplifying the equation gives $3nx + 5x = 30x + 2nx$, which reduces to $nx = 25x$.
• Dividing by $x$ yields $n = 25$, so the number of brown pairs is 25.
Why the other options are wrong
- (a) 10
- If $n=10$, the new bill is $35x$ and the original is $25x$, which is a 40% increase, not 100%.
- (b) 15
- If $n=15$, the new bill is $50x$ and the original is $30x$, which is a 66.67% increase, not 100%.
- (c) 20
- If $n=20$, the new bill is $65x$ and the original is $35x$, which is a 85.71% increase, not 100%.
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.