A shopkeeper sells an article at ₹ 40 and gets X% profit. However, when he sells it at ₹ 20, he faces same percentage of loss. What is the original cost of the article?
- (a) ₹ 10
- (b) ₹ 20
- (c) ₹ 30 ✓ UPSC's answer
- (d) ₹ 40
Why the answer is (c)
• Let the cost price (CP) be C and the profit/loss percentage be X%.
• Selling at ₹40 gives a profit of X%, so 40 = C(1 + X/100).
• Selling at ₹20 gives a loss of X%, so 20 = C(1 - X/100).
• Adding the two equations: 40 + 20 = C(1 + X/100) + C(1 - X/100).
• This simplifies to 60 = 2C, which means C = 30.
• Therefore, the original cost of the article is ₹30.
Why the other options are wrong
- (a) ₹ 10
- If the cost were ₹10, selling at ₹40 would yield a 300% profit, while selling at ₹20 would yield a 100% profit, not a loss.
- (b) ₹ 20
- If the cost were ₹20, selling at ₹20 would result in neither profit nor loss (0%), contradicting the condition of a loss.
- (d) ₹ 40
- If the cost were ₹40, selling at ₹40 would result in neither profit nor loss (0%), contradicting the condition of a profit.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2018, held on 3 June 2018. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.