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A merchant sells an item for Rs 450 at a loss of 10%. At what price should he sell it to gain 20%?
Rs 550
Rs 600
Rs 650
Rs 700
Rs 600
Use the ratio of percentages: The ratio of Selling Prices is equivalent to the ratio of (100 + Profit%) to (100 - Loss%). Simply compute 450├Ч(120/90)=450├Ч(4/3)=600.
Selling Price 1 = Rs 450, Loss percentage = 10%, Target Gain percentage = 20%.
SP2тАЛ=SP1тАЛ├Ч100тИТL1тАЛ100+G2тАЛтАЛ
Use the ratio of percentages: The ratio of Selling Prices is equivalent to the ratio of (100 + Profit%) to (100 - Loss%). Simply compute 450├Ч(120/90)=450├Ч(4/3)=600.
Students often calculate the loss on the Selling Price (Rs450) instead of the Cost Price, or accidentally multiply by 1.10 instead of dividing by 0.90.
Define the relationship between SP and CP
Since the item is sold at a loss of 10%, the selling price is 90% of the cost price. Let Cost Price be CP.
0.90├ЧCP=450
Calculate Cost Price
Solve for CP by dividing the selling price by 0.9.
CP=0.90450тАЛ=500
Calculate target Selling Price
To gain 20%, the new selling price should be 120% of the cost price.
SPnewтАЛ=500├Ч1.20=600
B is correct because the Cost Price is calculated to be Rs 500, and 120% of Rs 500 results in a selling price of Rs 600.
This ratio-based approach is identical to how currency conversion or time-speed-distance problems are solved using scaling factors.
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