A trader purchases 600 units of an item at ₹30 per unit. He sells 400 units at…
2025
A trader purchases 600 units of an item at ₹30 per unit. He sells 400 units at a profit of 20% and the remaining 200 units at a loss of 10%. What is his overall profit or loss percentage?
- A.
12% profit
- B.
10% profit
- C.
15% loss
- D.
8% loss
Show answer & explanation
Correct answer: B
When a trader sells goods in separate lots at different profit or loss percentages, the overall profit or loss percentage is not the simple average of the individual rates — it must be computed from the combined (total) cost price and the combined (total) selling price of every lot together: Overall % = ((Total SP − Total CP) / Total CP) × 100.
Total cost price of 600 units at ₹30 per unit: 600 × ₹30 = ₹18,000.
Selling price of the first lot — 400 units sold at 20% profit: unit price = ₹30 × 1.20 = ₹36, so lot revenue = 400 × ₹36 = ₹14,400.
Selling price of the second lot — 200 units sold at 10% loss: unit price = ₹30 × 0.90 = ₹27, so lot revenue = 200 × ₹27 = ₹5,400.
Total selling price of all 600 units: ₹14,400 + ₹5,400 = ₹19,800.
Overall profit = Total SP − Total CP = ₹19,800 − ₹18,000 = ₹1,800.
Overall profit percentage = (₹1,800 / ₹18,000) × 100 = 10%.
Cross-check: because both lots share the same ₹30 cost price per unit, the overall rate also equals the quantity-weighted average of the two individual rates: (400/600) × (+20%) + (200/600) × (−10%) = (2/3 × 20) + (1/3 × −10) = 13.33% − 3.33% = 10%, which matches the direct calculation above.
Overall result: the trader makes a 10% profit on the whole transaction.