Question 1

A vendor buys apples at ₹10 per kg and sells them at a profit of 25%. Due to wastage, he loses 5 kg out of every 100 kg purchased. What is his overall profit percentage?

Accepted Answer

Step 1: CP per kg = ₹10. SP per kg = 10 + (25% of 10) = ₹12.50. Step 2: Out of 100 kg purchased, only 95 kg are sold (5 kg wasted). Step 3: Total CP for 100 kg = 100 × 10 = ₹1000. Step 4: Total SP for 95 kg = 95 × 12.50 = ₹1187.50. Step 5: Profit = 1187.50 - 1000 = ₹187.50. Step 6: Profit% = (187.50/1000) × 100 = 18.75%. Therefore, the answer is 18.75%.

Question 2

A retailer buys a product for ₹300 and marks it up by 50%. He then offers a discount of 20% on the marked price. What is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹300. Step 2: Markup = 50% of 300 = ₹150, so Marked Price (MP) = 300 + 150 = ₹450. Step 3: Discount = 20% of 450 = ₹90, so Selling Price (SP) = 450 − 90 = ₹360. Step 4: Profit = SP − CP = 360 − 300 = ₹60. Step 5: Profit% = (Profit/CP) × 100 = (60/300) × 100 = 20%.

Question 3

A shopkeeper buys an item for ₹500. He marks it up by 20% and then gives a discount of 10% on the marked price. What is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹500. Step 2: Marked Price (MP) = 500 + (20% of 500) = 500 + 100 = ₹600. Step 3: Selling Price (SP) = 600 - (10% of 600) = 600 - 60 = ₹540. Step 4: Profit = SP - CP = 540 - 500 = ₹40. Step 5: Profit% = (40/500) × 100 = 8%. Therefore, the answer is 8%.

Question 4

A trader buys goods for ₹1000 and marks them up by 50%. He then offers a discount of 20% on the marked price. Later, he offers an additional discount of 10% on the already discounted price. What is his final profit percentage?

Accepted Answer

Step 1: CP = ₹1000. Step 2: MP = 1000 + (50% of 1000) = ₹1500. Step 3: After first discount of 20%: Price = 1500 - (20% of 1500) = 1500 - 300 = ₹1200. Step 4: After second discount of 10%: SP = 1200 - (10% of 1200) = 1200 - 120 = ₹1080. Step 5: Profit = 1080 - 1000 = ₹80. Step 6: Profit% = (80/1000) × 100 = 8%. Therefore, the answer is 8%.

Question 5

A shopkeeper first increases the price of an item by 30%, then decreases it by 20%. If the final price is ₹1040, what was the original price?

Accepted Answer

Step 1: Let original price = ₹x. Step 2: After 30% increase: Price = x + 0.30x = 1.30x. Step 3: After 20% decrease on increased price: Final Price = 1.30x - (20% of 1.30x) = 1.30x × 0.80 = 1.04x. Step 4: Given final price = ₹1040. Step 5: 1.04x = 1040 → x = 1040/1.04 = 1000. Therefore, original price = ₹1000.

Question 6

A store offers two successive discounts of 10% and 15% on an article marked at ₹1000. What is the final selling price?

Accepted Answer

Step 1: Marked Price (MP) = ₹1000. Step 2: After first discount of 10%: Price = 1000 × (1 − 0.10) = 1000 × 0.90 = ₹900. Step 3: After second discount of 15% on ₹900: Price = 900 × (1 − 0.15) = 900 × 0.85 = ₹765.

Question 7

If an article is sold at a discount of 30% on the marked price, the selling price is ₹280. What is the marked price?

Accepted Answer

Step 1: Discount = 30%, so SP = MP × (1 − 30/100) = MP × 0.70. Step 2: 280 = MP × 0.70. Step 3: MP = 280 ÷ 0.70 = ₹400.

Question 8

A trader buys 50 kg of rice at ₹40 per kg and sells it at ₹50 per kg. What is the total profit?

Accepted Answer

Step 1: Cost Price per kg = ₹40, Selling Price per kg = ₹50, Quantity = 50 kg. Step 2: Total CP = 40 × 50 = ₹2000. Step 3: Total SP = 50 × 50 = ₹2500. Step 4: Total Profit = SP - CP = 2500 - 2000 = ₹500. Therefore, the total profit is ₹500.

Question 9

A shopkeeper marks an item at ₹500 and gives a discount of 10%. He still makes a profit of 25%. What is the Cost Price of the item?

Accepted Answer

Step 1: Marked Price (MP) = ₹500, Discount = 10%, Profit = 25%. Step 2: Selling Price (SP) = MP × (1 - Discount%) = 500 × (1 - 0.10) = 500 × 0.9 = ₹450. Step 3: Profit = 25%, so SP = CP × (1 + Profit%) = CP × 1.25. Step 4: 450 = CP × 1.25. Step 5: CP = 450 / 1.25 = ₹360. Therefore, the Cost Price is ₹360.

Question 10

A merchant sells an item at a loss of 15%. If he had sold it for ₹120 more, he would have made a profit of 5%. What is the cost price of the item?

Accepted Answer

Step 1: Let Cost Price = ₹x. Step 2: At 15% loss, SP₁ = x - 0.15x = 0.85x. Step 3: At 5% profit, SP₂ = x + 0.05x = 1.05x. Step 4: Given SP₂ - SP₁ = 120. Step 5: 1.05x - 0.85x = 120 → 0.20x = 120 → x = 600. Therefore, Cost Price = ₹600.

Question 11

A vendor buys apples at ₹60 per dozen and sells them at ₹6 per apple. What is his profit percentage?

Accepted Answer

Step 1: CP per dozen = ₹60, so CP per apple = 60 / 12 = ₹5. Step 2: SP per apple = ₹6. Step 3: Profit per apple = 6 - 5 = ₹1. Step 4: Profit % = (1 / 5) × 100 = 20%. Therefore, the profit percentage is 20%.

Question 12

A shopkeeper buys a pen for ₹12 and sells it for ₹15. What is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹12, Selling Price (SP) = ₹15. Step 2: Profit = SP - CP = 15 - 12 = ₹3. Step 3: Profit % = (Profit / CP) × 100 = (3 / 12) × 100 = 25%. Therefore, the profit percentage is 25%.

Question 13

A book is sold at a loss of 20%. If the Selling Price is ₹240, what is the Cost Price?

Accepted Answer

Step 1: Loss = 20%, Selling Price (SP) = ₹240. Step 2: When there is a 20% loss, SP = CP × (1 - 20/100) = CP × 0.8. Step 3: 240 = CP × 0.8. Step 4: CP = 240 / 0.8 = ₹300. Therefore, the Cost Price is ₹300.

Question 14

A retailer buys an item for ₹400. He marks it up by 60% but then gives two successive discounts of 15% and 10%. What is his profit or loss percentage?

Accepted Answer

Step 1: CP = ₹400. Step 2: MP = 400 + (60% of 400) = 400 + 240 = ₹640. Step 3: After first discount of 15%: Price = 640 - (15% of 640) = 640 - 96 = ₹544. Step 4: After second discount of 10%: SP = 544 - (10% of 544) = 544 - 54.40 = ₹489.60. Step 5: Profit = 489.60 - 400 = ₹89.60. Step 6: Profit% = (89.60/400) × 100 = 22.4%. Therefore, the answer is 22.4%.

Question 15

A merchant buys notebooks at ₹8 each and sells them at ₹10 each. If he sells 200 notebooks, what is his profit percentage?

Accepted Answer

Step 1: CP per notebook = ₹8, SP per notebook = ₹10, Quantity = 200. Step 2: Profit per notebook = 10 - 8 = ₹2. Step 3: Profit % = (Profit per unit / CP per unit) × 100 = (2 / 8) × 100 = 25%. Therefore, the profit percentage is 25%.

Question 16

A shopkeeper marks an article at ₹500. He gives a discount of 20% on the marked price. What is the selling price?

Accepted Answer

Step 1: Marked Price (MP) = ₹500. Step 2: Discount = 20% of ₹500 = (20/100) × 500 = ₹100. Step 3: Selling Price (SP) = MP − Discount = 500 − 100 = ₹400.

Question 17

A merchant offers a discount of 25% on the marked price of a shirt. If the selling price is ₹450, what is the marked price?

Accepted Answer

Step 1: Discount = 25%, so SP = MP × (1 − 25/100) = MP × 0.75. Step 2: 450 = MP × 0.75. Step 3: MP = 450 ÷ 0.75 = ₹600.

Question 18

A shopkeeper buys a watch for ₹800 and marks it at 60% above the cost price. If he offers a discount of 25% on the marked price, what is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹800. Step 2: Marked Price (MP) = 800 + (60% of 800) = 800 + 480 = ₹1280. Step 3: Discount = 25% of 1280 = ₹320. Step 4: Selling Price (SP) = 1280 - 320 = ₹960. Step 5: Profit = 960 - 800 = ₹160. Step 6: Profit % = (160/800) × 100 = 20%.

Question 19

A retailer buys goods at ₹2400 per dozen. He marks them at 60% above cost price and offers a discount of 20% on the marked price. What is the selling price per item?

Accepted Answer

Step 1: Cost price per dozen = ₹2400, so CP per item = 2400/12 = ₹200. Step 2: Marked price per item = 200 × (1 + 0.60) = 200 × 1.60 = ₹320. Step 3: Selling price per item = 320 × (1 - 0.20) = 320 × 0.80 = ₹256.

Question 20

A shopkeeper marks his goods 50% above the cost price. What discount percentage should he offer to make a profit of 20%?

Accepted Answer

Step 1: Let Cost Price (CP) = ₹100. Step 2: Marked Price (MP) = 100 + (50% of 100) = 100 + 50 = ₹150. Step 3: Required Selling Price (SP) for 20% profit = 100 + (20% of 100) = 100 + 20 = ₹120. Step 4: Discount = MP - SP = 150 - 120 = ₹30. Step 5: Discount % = (30/150) × 100 = 20%.

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