A person sells his goods at a price 60% above the cost price. He sells 40% of…
2019
A person sells his goods at a price 60% above the cost price. He sells 40% of his goods at a 10% discount, 35% of his goods at a 20% discount, and the remaining portion at a 30% discount. What is his overall percentage profit?
- A.
31.8%
- B.
32.5%
- C.
31.2%
- D.
30.4%
Attempted by 29 students.
Show answer & explanation
Correct answer: D
Concept: When different portions of the same stock are sold at different discounts off one common marked price, the overall profit does not come from averaging the discounts directly — it comes from the weighted average selling price, where each portion's selling price is weighted by the fraction of goods sold at that price: Profit % = (Weighted average S.P. − C.P.) ÷ C.P. × 100.
Application:
Let the cost price (C.P.) = ₹100 for easy calculation.
Marked price (M.P.) is 60% above cost, so M.P. = 100 × 1.6 = ₹160.
40% of the goods sold at a 10% discount: S.P.₁ = 160 × 0.9 = ₹144.
35% of the goods sold at a 20% discount: S.P.₂ = 160 × 0.8 = ₹128.
Remaining 25% of the goods sold at a 30% discount: S.P.₃ = 160 × 0.7 = ₹112.
Weighted average S.P. = (0.40 × 144) + (0.35 × 128) + (0.25 × 112) = 57.6 + 44.8 + 28 = ₹130.4.
Overall profit = 130.4 − 100 = 30.4, so the overall percentage profit is 30.4%.
Cross-check (fraction method): Express the goods-shares and discount multipliers as fractions: 40% = 2/5 with multiplier 9/10, 35% = 7/20 with multiplier 4/5, and 25% = 1/4 with multiplier 7/10. The combined multiplier on the marked price is (2/5 × 9/10) + (7/20 × 4/5) + (1/4 × 7/10) = 18/50 + 28/100 + 7/40 = 72/200 + 56/200 + 35/200 = 163/200 = 0.815. Applying this to the 1.6 mark-up factor gives 1.6 × 0.815 = 1.304, i.e. a 30.4% profit — confirming the result above.