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A shopkeeper sold an article for ₹XXX. If he had sold it for ₹YYY, he would have gained Z%. What was the cost price of the article?
Profit, ₹123
Loss, ₹123
Loss, ₹100
Profit, ₹100
Profit, ₹100
Calculate cost price of shirt: 960 / 0.96 = 1000. Calculate cost price of sweater: 840 / 1.2 = 700. Total CP = 1700, Total SP = 960 + 840 = 1800. Net Profit = 1800 - 1700 = 100.
Shirt sold at ₹960 (4% loss). Sweater sold at ₹840 (20% profit).
CP=100±profit/loss %SP×100
Calculate cost price of shirt: 960 / 0.96 = 1000. Calculate cost price of sweater: 840 / 1.2 = 700. Total CP = 1700, Total SP = 960 + 840 = 1800. Net Profit = 1800 - 1700 = 100.
Students often make mistakes in calculating profit/loss on total sales by incorrectly calculating the cost price percentage or confusing 4% loss as 0.04 instead of 0.96 multiplier.
Calculate CP of the shirt
Given SP = ₹960 and Loss = 4%. So, CP = 960 / (1 - 0.04) = 960 / 0.96.
CPshirt=0.96960=1000
Calculate CP of the sweater
Given SP = ₹840 and Profit = 20%. So, CP = 840 / (1 + 0.20) = 840 / 1.2.
CPsweater=1.2840=700
Calculate total CP and total SP
Total CP = 1000 + 700 = 1700. Total SP = 960 + 840 = 1800.
Total CP=1700,Total SP=1800
Find Net Profit or Loss
Since Total SP > Total CP, it is a profit. Profit = 1800 - 1700 = 100.
Profit=1800−1700=100
D is correct because the total cost price is ₹1700 and the total selling price is ₹1800, resulting in a net profit of ₹100.
This type of arithmetic problem is fundamental to percentage-based topics like simple interest and discount calculations in competitive exams.
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