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A shopkeeper sells an item for Rs. 840 at a loss of 16%. What should be the selling price to gain 10%?
Rs.┬а1100
Rs.┬а1050
Rs.┬а1200
Rs.┬а1150
Rs.┬а1100
Equate the selling price directly to its percentage value: (100тИТ16)%=84%, so 84%=840, which means 1%=10. For a 10% gain, the new selling price is 110%=110imes10=Rs.┬а1100.
Selling Price (SP1) = Rs. 840, Loss percentage = 16%, Desired Gain percentage = 10%
SP=100100┬▒extProfit/Loss%тАЛimes┬аCP
Equate the selling price directly to its percentage value: (100тИТ16)%=84%, so 84%=840, which means 1%=10. For a 10% gain, the new selling price is 110%=110imes10=Rs.┬а1100.
Students often calculate 10% profit directly on the given selling price (Rs. 840) instead of finding the Cost Price first or using the direct percentage equivalence.
Find Cost Price from the first selling price
Since there is a 16% loss, the selling price is 84% of the cost price. We can set up the equation: 0.84imesCP=840.
CP=0.84840тАЛ=1000
Calculate the new Selling Price for 10% gain
To gain 10%, the new selling price must be 110% of the cost price. Multiply the cost price by 1.10.
SP2тАЛ=1000imes100110тАЛ=1100
A is correct because the cost price is calculated as Rs. 1000, and a 10% gain on this gives a new selling price of Rs. 1100.
This direct percentage equivalence shortcut can also be applied to discount, marked price, and simple interest problems to save valuable time in competitive exams.
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