Discussion
By selling an article at 72 % of its selling price, a shopkeeper loses 12 %. If he sells it at 10 % less than its original selling price, then what will be his profit percent?
Answer: A
The profit is 10 %. Selling at 72 % of the selling price gives a loss of 12 %, so 0.72 of the selling price equals 0.88 of the cost price.
\[ 0.72\,SP = 0.88\,CP \Rightarrow SP = \frac{11}{9}\,CP \]
Selling at 10 % less than the original selling price gives 0.9 x (11/9) CP = 1.1 CP. That is a profit of 10 % on the cost price.
The options 12 %, 9 % and 8 % do not agree with 1.1 times the cost price, so the first option is the answer. As a check, take the cost price as 90. The selling price is then 110, and 72 % of 110 is 79.2, which is 12 % below 90. At 10 % less than 110, which is 99, the profit is 9 on 90, or 10 %.
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