Question
A shopkeeper bought a batch of shirts for ₹2,000. He
sold 60% of the shirts at a 20% profit, and the remaining 40% of the shirts at a 10% loss. Find the overall profit or loss percentage on the entire batch of shirts.Solution
ATQ, Step 1: Calculate the profit on 60% of the shirts sold at a 20% profit: Profit Percentage = 20% Cost Price (CP) = ₹2,000 Percentage of shirts sold at a profit = 60% Profit on 60% of shirts = (Profit Percentage / 100) × (Cost Price) * (Percentage of shirts sold at a profit) Profit on 60% of shirts = (20 / 100) * (₹2,000) × (60 / 100) Step 2: Calculate the loss on 40% of the shirts sold at a 10% loss: Loss Percentage = 10% Cost Price (CP) = ₹2,000 Percentage of shirts sold at a loss = 40% Loss on 40% of shirts = (Loss Percentage / 100) × (Cost Price) * (Percentage of shirts sold at a loss) Loss on 40% of shirts = (10 / 100) × (₹2,000) × (40 / 100) Step 3: Calculate the overall profit or loss: Overall Profit/Loss = (Profit on 60% of shirts) - (Loss on 40% of shirts) Now, plug in the values calculated in Step 1 and Step 2: Overall Profit/Loss = [(20 / 100) × (₹2,000) × (60 / 100)] - [(10 / 100) × (₹2,000) × (40 / 100)] Now, calculate the values: Overall Profit/Loss = (₹240) - (₹80) Overall Profit/Loss = ₹240 - ₹80 = ₹160 Step 4: Calculate the profit or loss percentage on the entire batch: Profit Percentage = (Overall Profit / Total Cost Price) × 100 Profit Percentage = (₹160 / ₹2,000) × 100 Profit Percentage = (0.08) × 100 Profit Percentage = 8% So, the overall profit percentage on the entire batch of shirts is 8%.
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