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A merchant sells an item for Rs. 480, incurring a loss of 20%. At what price should he sell it to gain a profit of 10%?
Rs. 600
Rs. 660
Rs. 720
Rs. 580
Rs. 660
Use the ratio: SP2тАЛSP1тАЛтАЛ=100+P2тАЛ100тИТL1тАЛтАЛ. Here, SP2тАЛ480тАЛ=11080тАЛ. Since 80├Ч6=480, then 110├Ч6=660.
Selling Price (SP1) = Rs. 480, Loss percentage = 20%, Target Profit percentage = 10%.
SP2тАЛ=SP1тАЛ├Ч100тИТL1тАЛ100+P2тАЛтАЛ
Use the ratio: SP2тАЛSP1тАЛтАЛ=100+P2тАЛ100тИТL1тАЛтАЛ. Here, SP2тАЛ480тАЛ=11080тАЛ. Since 80├Ч6=480, then 110├Ч6=660.
Calculating 10% profit on the selling price (Rs. 480) instead of the cost price, which leads to an incorrect value.
Analyze the initial loss scenario
A loss of 20% means the selling price is 80% of the cost price (CP).
SP1тАЛ=0.80├ЧCPтЗТ480=0.80├ЧCP
Calculate the Cost Price (CP)
Solve for CP by dividing the selling price by 0.80.
CP=0.80480тАЛ=600
Calculate the new selling price for 10% profit
For a 10% profit, the new selling price (SP2) must be 110% of the cost price.
SP2тАЛ=1.10├Ч600=660
B is correct because applying the direct ratio formula yields a selling price of Rs. 660 for a 10% profit.
This concept of base-value comparison is identical to solving 'Discount' problems where you convert Marked Price to Cost Price using similar ratio multipliers.
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