A person marks his goods 40% above the cost price. He sold 30% of the goods at…
2019
A person marks his goods 40% above the cost price. He sold 30% of the goods at the marked price, 60% of the goods at a discount of 20%, and the remaining 10% of the goods at a discount of 40%. What is 60% of his overall gain percent?
Answer: D. 10.56% — Concept: When goods are sold in separate quantity-based batches at different discounts off the same marked price, the overall gain percent equals (total…
- A.
13.15%
- B.
15.18%
- C.
17.14%
- D.
10.56%
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Correct answer: D
Concept: When goods are sold in separate quantity-based batches at different discounts off the same marked price, the overall gain percent equals (total revenue − total cost) ÷ total cost × 100, where each batch's selling price = marked price × (1 − discount%).
Assume total goods = 100 units at a cost price of ₹100 each, so total cost price = ₹10,000. Marked price = 140% of cost price = ₹140 per unit.
Batch 1 — 30 units sold at the marked price: revenue = 30 × ₹140 = ₹4,200.
Batch 2 — 60 units sold at 20% discount on the marked price: selling price = ₹140 × 0.8 = ₹112; revenue = 60 × ₹112 = ₹6,720.
Batch 3 — the remaining 10 units sold at 40% discount on the marked price: selling price = ₹140 × 0.6 = ₹84; revenue = 10 × ₹84 = ₹840.
Total revenue = ₹4,200 + ₹6,720 + ₹840 = ₹11,760. Overall gain = ₹11,760 − ₹10,000 = ₹1,760, so overall gain percent = 17.6%.
The question asks for 60% of the overall gain percent: 0.6 × 17.6% = 10.56%.
Cross-check: each batch's own gain on ₹100 cost is +40% (30 units), +12% (60 units, since ₹112 vs ₹100), and −16% (10 units, since ₹84 vs ₹100). Weighting by quantity share: 0.30×40 + 0.60×12 + 0.10×(−16) = 12 + 7.2 − 1.6 = 17.6%, confirming the overall gain percent and the final value of 10.56%.