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A shopkeeper sells an item for Rs 450 at a loss of 10%. What should be the selling price to gain 10%?
Rs┬а550
Rs┬а500
Rs┬а600
Rs┬а525
Rs┬а550
Use the direct proportion shortcut: SP2 = SP1 * (100 + Gain%) / (100 - Loss%) to skip finding the cost price.
Selling price SP1 = Rs 450, Loss percentage = 10%, Desired gain percentage = 10%
SP2тАЛ=SP1тАЛ├Ч100тИТLoss%100+Gain%тАЛ
Use the direct proportion shortcut: SP2 = SP1 * (100 + Gain%) / (100 - Loss%) to skip finding the cost price.
Students often add 10% directly to the selling price instead of calculating the cost price first or using the direct ratio formula.
Identify Given Values
Note the initial selling price and the loss percentage given in the problem statement.
SP1тАЛ=Rs┬а450,Loss%=10%
Apply Ratio Formula
Use the direct relation between selling prices at different profit/loss percentages to find the new selling price.
SP2тАЛ=450├Ч100тИТ10100+10тАЛ
Calculate Final Value
Simplify the fraction and multiply to get the required selling price.
SP2тАЛ=450├Ч90110тАЛ=450├Ч911тАЛ=550
A is correct because the required selling price to achieve a 10% gain is Rs 550.
Mastering percentage-based multipliers helps solve discount, markup, and partnership problems quickly in competitive exams.
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