Question 1

A vendor buys oranges at ₹40 per dozen. He sells them at ₹5 per orange. Due to spoilage, he loses 10% of the oranges. What is his profit percentage on the cost price?

Accepted Answer

Step 1: CP per dozen = ₹40. CP per orange = 40/12 = ₹10/3 ≈ ₹3.33. Step 2: SP per orange = ₹5. Step 3: For 12 oranges (1 dozen): CP = ₹40. After 10% loss, he has 90% of 12 = 10.8 oranges. Step 4: SP = 10.8 × 5 = ₹54. Step 5: Profit = 54 - 40 = ₹14. Step 6: Profit % = (14/40) × 100 = 35%. Therefore, the answer is 35% profit.

Question 2

A retailer buys a product at ₹600 per unit. He marks it up by 60% and offers a discount of 15%. He then sells the remaining stock at a further discount of 10% on the already discounted price. If he sells 100 units in the first transaction and 80 units in the second transaction, what is his total profit?

Accepted Answer

Step 1: CP per unit = ₹600. MP = 600 + 60% of 600 = 600 × 1.6 = ₹960. Step 2: First SP (after 15% discount) = 960 - 15% of 960 = 960 × 0.85 = ₹816. Step 3: Profit per unit (first transaction) = 816 - 600 = ₹216. Total profit (100 units) = 216 × 100 = ₹21,600. Step 4: Second SP (after 10% further discount) = 816 - 10% of 816 = 816 × 0.9 = ₹734.40. Step 5: Profit per unit (second transaction) = 734.40 - 600 = ₹134.40. Total profit (80 units) = 134.40 × 80 = ₹10,752. Step 6: Total profit = 21,600 + 10,752 = ₹32,352. Therefore, the answer is ₹32,352.

Question 3

A shopkeeper buys an article at ₹500. He marks it up by 40%, then offers a discount of 10% on the marked price. Later, he realizes demand is high and increases the selling price by 20%. What is his overall profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹500. Step 2: Marked Price (MP) = 500 + 40% of 500 = 500 × 1.4 = ₹700. Step 3: After 10% discount, Selling Price (SP₁) = 700 × 0.9 = ₹630. Step 4: After 20% increase, Final SP = 630 × 1.2 = ₹756. Step 5: Profit = 756 − 500 = ₹256. Step 6: Profit % = (256/500) × 100 = 51.2%.

Question 4

A retailer purchases items at ₹500 each. He sells 30% of items at 40% profit, 50% of items at 20% profit, and the remaining items at a loss. If his overall profit is 8%, at what loss percentage does he sell the remaining items?

Accepted Answer

Step 1: Let total items = 100. CP per item = ₹500. Total CP = 100 × 500 = ₹50,000. Step 2: First batch: 30 items at 40% profit. SP = 500 × 1.4 = ₹700 per item. Revenue = 30 × 700 = ₹21,000. Profit = 30 × 200 = ₹6,000. Step 3: Second batch: 50 items at 20% profit. SP = 500 × 1.2 = ₹600 per item. Revenue = 50 × 600 = ₹30,000. Profit = 50 × 100 = ₹5,000. Step 4: Third batch: 20 items at loss. Total profit required = 8% of 50,000 = ₹4,000. Profit from first two batches = 6,000 + 5,000 = ₹11,000. Loss from third batch = 11,000 − 4,000 = ₹7,000. Step 5: Loss per item = 7,000/20 = ₹350. Loss % = (350/500) × 100 = 70%.

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