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A shopkeeper sells an item for Rs. 900 at a loss of 10%. At what price should he sell it to gain 10%?
Rs.┬а1000
Rs.┬а1100
Rs.┬а1200
Rs.┬а1050
Rs.┬а1100
Since loss is 10%, the given SP is 90% of Cost Price. To gain 10%, the required SP is 110% of Cost Price. Directly calculate Required┬аSP=900├Ч90110тАЛ.
Selling price at 10% loss = Rs. 900, Loss percentage = 10%, Desired profit percentage = 10%
SP=CP├Ч(1┬▒100Profit/Loss%тАЛ)
Since loss is 10%, the given SP is 90% of Cost Price. To gain 10%, the required SP is 110% of Cost Price. Directly calculate Required┬аSP=900├Ч90110тАЛ.
Students often calculate 10% profit directly on the given selling price (Rs. 900) instead of first finding the cost price or using the direct proportionality to cost price.
Find the Cost Price
At a 10% loss, the selling price is 90% of the cost price (CP). Setting up the equation: 900=CP├Ч10090тАЛ.
CP=90900├Ч100тАЛ=1000
Calculate the Desired Selling Price
To achieve a 10% profit, the new selling price should be 110% of the cost price (CP=1000).
SP2тАЛ=1000├Ч100110тАЛ=1100
B is correct because the required selling price to gain 10% is calculated as Rs. 1100.
This direct ratio approach of comparing percentages of a common base value can also be applied to discount, markup, and simple interest problems.
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