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An item is sold at a loss of 15%. If it were sold for Rs. 100 more, there would be a profit of 5%. What is the cost price?
Rs.┬а500
Rs.┬а600
Rs.┬а450
Rs.┬а550
Rs.┬а500
Sum the loss and profit percentages to find the total percentage difference corresponding to the extra amount: 20%┬аof┬аCP=100тЯ╣CP=500.
Loss = 15%, Profit = 5%, Difference in selling price = Rs. 100
CP=Profit%+extLoss%DifferenceтАЛimes100
Sum the loss and profit percentages to find the total percentage difference corresponding to the extra amount: 20%┬аof┬аCP=100тЯ╣CP=500.
Subtracting the loss percentage from the profit percentage instead of adding them when crossing from negative to positive.
Analyze Given Data
Let the cost price be CP. A loss of 15% means SP1тАЛ=0.85imesCP, and a profit of 5% means SP2тАЛ=1.05imesCP.
SP2тАЛтИТSP1тАЛ=1.05imes┬аCPтИТ0.85imes┬аCP=0.20imes┬аCP
Set Up Equation
The difference between the two selling prices is given as Rs. 100.
0.20imes┬аCP=100
Solve for Cost Price
Divide 100 by 0.20 to find the cost price.
CP=0.20100тАЛ=500
Verify Option
The calculated cost price is Rs. 500, which corresponds to Option A.
CP=Rs.┬а500
A is correct because the 20% total variation between a 15% loss and 5% profit equals Rs. 100, making the cost price Rs. 500.
Understanding percentage gaps across a zero baseline is also very useful for break-even analysis and simple interest variation problems.
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