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A merchant sells 40% of his stock at a 25% profit, 30% of the remaining stock at a 20% profit, and the rest at a 10% loss. What is his overall percentage profit?
10.8%
11.2%
9.6%
12.4%
11.2%
Assume total stock = 100 units at Rs 100 cost. Calculate net profit: (400.25) + (180.20) + (42*-0.10). Sum = 10 + 3.6 - 4.2 = 11.2.
40% of stock sold at 25% profit, 30% of remaining stock at 20% profit, and the rest at 10% loss.
Overall┬аProfit%┬а=тИС(wiтАЛ├ЧpiтАЛ)
Assume total stock = 100 units at Rs 100 cost. Calculate net profit: (400.25) + (180.20) + (42*-0.10). Sum = 10 + 3.6 - 4.2 = 11.2.
Many students calculate 30% of the total stock instead of 30% of the remaining 60% stock, leading to incorrect profit distributions.
Calculate the stock segments
Assume total stock is 100 units. First part is 40 units. Remaining stock is 100тИТ40=60 units. Second part is 30%┬аof┬а60=18 units. Third part is the rest, which is 100тИТ(40+18)=42 units.
Part┬а1=40,Part┬а2=18,Part┬а3=42
Calculate individual profits/losses
Calculate profit for each segment based on the percentage gain or loss provided.
P1тАЛ=40├Ч0.25=10,P2тАЛ=18├Ч0.20=3.6,P3тАЛ=42├Ч(тИТ0.10)=тИТ4.2
Calculate total percentage profit
Sum all values to find the overall net profit. Since total base is 100, the sum is directly the percentage.
Net┬аProfit=10+3.6тИТ4.2=11.2%
B is correct because the weighted average of the profit margins results in a total profit of 11.2%.
This concept of 'weighted averages' is frequently used in Mixture and Alligation problems in Competitive Quantitative Aptitude sections.