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A shopkeeper bought 50 mangoes at ₹10 each. He sold 30 mangoes at a profit of 20% and the remaining 20 mangoes at a loss of 10%. What is his overall profit or loss percentage?
8% profit
2% loss
4% profit
6% loss
8% profit
Use the weighted average of percentages: 50(30×20%)+(20×−10%)=50600−200=50400=8%.
Total mangoes = 50, Cost price per mango = ₹10. 30 mangoes sold at 20% profit, 20 mangoes sold at 10% loss.
Overall Profit/Loss=Total CP(Profit1+Profit2)×100
Use the weighted average of percentages: 50(30×20%)+(20×−10%)=50600−200=50400=8%.
Students often calculate the profit on 30 and loss on 20 separately and divide by the individual quantities (30 or 20) instead of the total quantity (50).
Calculate total cost price
The total number of mangoes is 50 and the cost price of each is ₹10.
Total CP=50×10=500
Calculate profit from the first batch
30 mangoes are sold at a 20% profit. CP of 30 mangoes is 300.
Profit1=300×0.20=60
Calculate loss from the second batch
The remaining 20 mangoes are sold at a 10% loss. CP of 20 mangoes is 200.
Loss2=200×0.10=20
Calculate net profit and percentage
Net profit is the difference between gain and loss. Divide by total CP for the final percentage.
Overall Profit=60−20=40;Profit %=50040×100=8%
A is correct because the net profit of ₹40 on a total cost of ₹500 results in an overall profit of 8%.
This concept of weighted averages is identical to calculating the combined mean in Statistics and the final concentration in Mixtures and Alligations.
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