Question 1

A shopkeeper buys an item for ₹500. He marks it up by 20% and then offers a discount of 10% on the marked price. What is his overall 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) after 10% discount = 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 2

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 3

If the marked price of a book is ₹450 and a discount of 15% is given, what amount does the customer pay?

Accepted Answer

Step 1: Marked Price (MP) = ₹450. Step 2: Discount = 15% of ₹450 = (15/100) × 450 = ₹67.50. Step 3: Amount paid (SP) = MP − Discount = 450 − 67.50 = ₹382.50. Therefore, the customer pays ₹382.50.

Question 4

The marked price of a shirt is ₹1000. After giving two successive discounts of 10% and 5%, what is the final selling price?

Accepted Answer

Step 1: Marked Price (MP) = ₹1000. Step 2: After first discount of 10%: Price = 1000 − (10% of 1000) = 1000 − 100 = ₹900. Step 3: After second discount of 5% on ₹900: Price = 900 − (5% of 900) = 900 − 45 = ₹855. Therefore, the final selling price is ₹855.

Question 5

If the cost price of 8 articles is equal to the selling price of 10 articles, what is the loss percentage?

Accepted Answer

Step 1: Let CP of 1 article = ₹1. Then CP of 8 articles = ₹8. Step 2: SP of 10 articles = ₹8 (given that CP of 8 = SP of 10). Step 3: SP of 1 article = 8/10 = ₹0.80. Step 4: Loss per article = 1 - 0.80 = ₹0.20. Step 5: Loss % = (0.20 / 1) × 100 = 20%. Therefore, the loss percentage is 20%.

Question 6

A merchant sells an article at a loss of 15%. If he had sold it for ₹80 more, he would have made a profit of 5%. What is the cost price of the article?

Accepted Answer

Step 1: Let CP = 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 = 80, so 1.05x - 0.85x = 80. Step 5: 0.20x = 80, therefore x = 400. The cost price is ₹400.

Question 7

A merchant purchases a book for ₹80 and wants to make a profit of 40%. At what price should he sell the book?

Accepted Answer

Step 1: Cost Price (CP) = ₹80, Required Profit % = 40%. Step 2: Profit = (40/100) × 80 = ₹32. Step 3: Selling Price (SP) = CP + Profit = 80 + 32 = ₹112. Therefore, the book should be sold for ₹112.

Question 8

The cost price of an item is ₹800 and it is sold at a profit of 25%. What is the selling price?

Accepted Answer

Step 1: Cost Price (CP) = ₹800. Step 2: Profit = 25% of ₹800 = (25/100) × 800 = ₹200. Step 3: Selling Price (SP) = CP + Profit = 800 + 200 = ₹1000. Therefore, the selling price is ₹1000.

Question 9

A retailer sells an item for ₹720 at a loss of 10%. What was the cost price of the item?

Accepted Answer

Step 1: Selling Price (SP) = ₹720, Loss = 10%. Step 2: When there is a loss of 10%, SP = CP − 10% of CP = 90% of CP. Step 3: 0.90 × CP = 720. Step 4: CP = 720/0.90 = ₹800. Therefore, the cost price is ₹800.

Question 10

A trader buys 5 kg of sugar for ₹250. He sells 2 kg at ₹60 per kg and the remaining at ₹45 per kg. What is his overall profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹250 for 5 kg. Step 2: Selling Price (SP) = (2 × 60) + (3 × 45) = 120 + 135 = ₹255. Step 3: Profit = SP - CP = 255 - 250 = ₹5. Step 4: Profit % = (5 / 250) × 100 = 2%. Therefore, the profit percentage is 2%.

Question 11

A shopkeeper marks an item at ₹500. He gives a discount of 20% on the marked price. If his cost price is ₹350, what is his profit percentage?

Accepted Answer

Step 1: Marked Price (MP) = ₹500, Discount = 20%. Step 2: Selling Price (SP) = MP - (20/100) × MP = 500 - 100 = ₹400. Step 3: Cost Price (CP) = ₹350. Step 4: Profit = SP - CP = 400 - 350 = ₹50. Step 5: Profit % = (50 / 350) × 100 = 14.29% ≈ 14.3% or 100/7 %. Therefore, the profit percentage is approximately 14.3%.

Question 12

A vendor sells an item at ₹450 and incurs a loss of 10%. What was the cost price of the item?

Accepted Answer

Step 1: Selling Price (SP) = ₹450, Loss % = 10%. Step 2: When there is a 10% loss, SP = CP × (90/100). Step 3: 450 = CP × 0.9, so CP = 450 / 0.9 = ₹500. Therefore, the cost price is ₹500.

Question 13

A merchant buys goods for ₹1200 and marks them at ₹1600. If he offers a discount of 10%, what is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹1200, Marked Price (MP) = ₹1600. Step 2: Discount = 10% of ₹1600 = (10/100) × 1600 = ₹160. Step 3: Selling Price (SP) = 1600 − 160 = ₹1440. Step 4: Profit = SP − CP = 1440 − 1200 = ₹240. Step 5: Profit% = (Profit/CP) × 100 = (240/1200) × 100 = 20%. Therefore, profit percentage is 20%.

Question 14

A dishonest shopkeeper claims to sell goods at cost price but uses a false weight of 800 g instead of 1000 g. What is his profit percentage?

Accepted Answer

Step 1: The shopkeeper gives only 800 g but charges for 1000 g. Step 2: If cost price per gram is C, then cost to shopkeeper = 800C, but selling price = 1000C. Step 3: Profit = 1000C - 800C = 200C. Step 4: Profit % = (200C / 800C) × 100 = 25%.

Question 15

A fraudulent dealer uses 900 g weights instead of 1 kg while buying goods at cost price. When selling, he uses correct weights but claims to sell at cost price. What is his overall profit percentage?

Accepted Answer

Step 1: While buying: He pays for 900 g but receives 1000 g (uses 900 g weight). Cost to him = 900 units for 1000 g goods. Step 2: While selling: He gives 1000 g at cost price of 1000 units (correct weight). Step 3: His cost per gram = 900/1000 = 0.9 units. Step 4: His selling price per gram = 1000/1000 = 1 unit. Step 5: Profit % = [(1 - 0.9) / 0.9] × 100 = (0.1/0.9) × 100 = 11.11% ≈ 11.11%.

Question 16

A dealer uses 950 g weights instead of 1000 g while buying goods. He sells at cost price using correct weights. What is his profit percentage?

Accepted Answer

Step 1: While buying, he uses 950 g weight, so he pays for 950 g but receives 1000 g. Step 2: Cost to him = 950 units for 1000 g goods. Step 3: While selling, he uses correct 1000 g weight and sells at cost price. Step 4: Selling price = 1000 units for 1000 g. Step 5: Cost per gram = 950/1000 = 0.95 units. Step 6: Selling price per gram = 1000/1000 = 1 unit. Step 7: Profit % = [(1 - 0.95) / 0.95] × 100 = (0.05/0.95) × 100 = 5.26%.

Question 17

A dishonest dealer uses 750 g weights instead of 1000 g while buying and uses 1000 g weights instead of 1250 g while selling. He claims to sell at cost price. What is his profit percentage?

Accepted Answer

Step 1: While buying: He uses 750 g weight, so he pays for 750 g but receives 1000 g. Cost = 750 units for 1000 g goods. Step 2: While selling: He uses 1000 g weight instead of 1250 g, so he gives 1000 g but charges for 1250 g. Revenue = 1250 units for 1000 g goods. Step 3: Cost per gram = 750/1000 = 0.75 units. Step 4: Selling price per gram = 1250/1000 = 1.25 units. Step 5: Profit per gram = 1.25 - 0.75 = 0.5 units. Step 6: Profit % = (0.5 / 0.75) × 100 = 66.67%.

Question 18

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. Therefore, the selling price is ₹400.

Question 19

A trader sells a watch for ₹1,200 at a loss of 20%. What was the cost price of the watch?

Accepted Answer

Step 1: Selling Price (SP) = ₹1,200, Loss = 20%. Step 2: If loss is 20%, then SP = 80% of CP. Step 3: 1,200 = 0.80 × CP. Step 4: CP = 1,200 / 0.80 = ₹1,500. Therefore, the cost price is ₹1,500.

Question 20

A book is marked at ₹500. A shopkeeper gives a discount of 15% on the marked price and still makes a profit of 25%. What is the cost price of the book?

Accepted Answer

Step 1: Marked Price (MP) = ₹500, Discount = 15%. Step 2: Selling Price (SP) = 500 - (0.15 × 500) = 500 - 75 = ₹425. Step 3: Profit = 25%, so SP = 1.25 × CP. Step 4: 425 = 1.25 × CP. Step 5: CP = 425 / 1.25 = ₹340. Therefore, the cost price is ₹340.

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