Question 1

A shopkeeper marks a sweater at ₹800. He offers a discount of 15% on the marked price. What is the selling price of the sweater?

Accepted Answer

Step 1: Marked Price (MP) = ₹800
Step 2: Discount = 15% of MP = 15% of 800 = (15/100) × 800 = ₹120
Step 3: Selling Price (SP) = MP - Discount = 800 - 120 = ₹680
Alternatively, SP = MP × (100 - Discount%)/100 = 800 × 85/100 = ₹680
Therefore, the selling price is ₹680.

Question 2

A shopkeeper marks an article at ₹2,500. He offers a discount of 12% on the marked price. However, he still makes a profit of 25% on the cost price. If he gives an additional discount of 4% on the already discounted price to a bulk buyer, what is the cost price of the article?

Accepted Answer

Step 1: Marked Price (MP) = ₹2,500. After 12% discount, Selling Price (SP₁) = 2,500 × (1 - 0.12) = 2,500 × 0.88 = ₹2,200. Step 2: This SP₁ gives 25% profit, so SP₁ = CP × 1.25. Therefore, 2,200 = CP × 1.25, which gives CP = 2,200 ÷ 1.25 = ₹1,760. Step 3: The additional 4% discount on ₹2,200 is irrelevant to finding the cost price — it only affects the final SP for the bulk buyer. The cost price remains ₹1,760.

Question 3

A shopkeeper marks an article at ₹2,500. He offers a discount of 20% on the marked price. However, he still makes a profit of 25% on the cost price. If he gives an additional discount of 5% on the already discounted price to a bulk buyer, what is the cost price of the article?

Accepted Answer

Step 1: Marked Price (MP) = ₹2,500. After 20% discount, Selling Price (SP₁) = 2,500 × 0.80 = ₹2,000. Step 2: This SP₁ gives 25% profit, so Cost Price (CP) = 2,000 ÷ 1.25 = ₹1,600. Step 3: The additional 5% discount is offered on the already discounted price (₹2,000), not on the original MP or CP, but the question asks for CP which remains ₹1,600 regardless of further discounts. Therefore, the cost price is ₹1,600.

Question 4

A retailer buys articles at ₹80 per piece. He marks them at a price such that after giving a discount of 25%, he still makes a profit of 20%. Later, he decides to give an additional 10% discount on the already discounted price. What is his new profit or loss percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹80. Required Selling Price for 20% profit = 80 × 1.20 = ₹96. Step 2: If SP = ₹96 after 25% discount, then MP × 0.75 = 96, so MP = 96/0.75 = ₹128. Step 3: After additional 10% discount on discounted price: New SP = 96 × 0.90 = ₹86.40. Step 4: Profit = 86.40 − 80 = ₹6.40. Profit % = (6.40/80) × 100 = 8%.

Question 5

A shopkeeper buys goods at ₹60 per kg. He marks them at ₹100 per kg. He sells 80% of the stock at a discount of 20% and the remaining 20% at a discount of 10%. What is his overall profit percentage?

Accepted Answer

Step 1: CP = ₹60/kg, MP = ₹100/kg. Assume 100 kg stock. Step 2: 80 kg at 20% discount: SP = ₹80/kg, Revenue = ₹6400. Step 3: 20 kg at 10% discount: SP = ₹90/kg, Revenue = ₹1800. Step 4: Total revenue = ₹8200, Total cost = ₹6000. Step 5: Profit % = (2200/6000) × 100 = 36⅔% ≈ 36.67%.

Question 6

A merchant offers a discount of 30% on marked price. After giving this discount, he earns a profit of 5%. If he wants to earn a profit of 20% instead, what discount percentage should he offer on the same marked price?

Accepted Answer

Step 1: Let CP = 100, MP = M. At 30% discount: SP = 0.70M. Given profit = 5%, so SP = 105. Thus 0.70M = 105 → M = 150. Step 2: For 20% profit: SP_new = 120. Step 3: Discount% = [(150 - 120)/150] × 100 = (30/150) × 100 = 20%.

Question 7

A shopkeeper marks goods 60% above cost price. He gives a discount of x% on marked price. If the profit earned is 8%, what is the value of x?

Accepted Answer

Step 1: Let CP = 100. Then MP = 160. Step 2: At x% discount: SP = 160(1 - x/100) = 160 - 1.6x. Step 3: Given profit = 8%, so SP = 108. Step 4: 160 - 1.6x = 108 → 1.6x = 52 → x = 32.5.

Question 8

A merchant offers a discount of 30% on the marked price. Even after this discount, he makes a profit of 40% on the cost price. If the cost price of an item is ₹350, what is the marked price?

Accepted Answer

Step 1: Cost Price (CP) = ₹350. For 40% profit: Selling Price (SP) = 350 × 1.40 = ₹490. Step 2: If SP is after 30% discount on MP, then SP = MP × 0.70. Step 3: 490 = MP × 0.70, so MP = 490/0.70 = ₹700.

Question 9

A shopkeeper marks up goods by 80% above cost price. He offers two successive discounts of 25% and 15% to customers. If a customer pays ₹918 for an article, what is the cost price of that article?

Accepted Answer

Step 1: Let cost price = CP. Marked price = CP + 80% of CP = 1.8 × CP. Step 2: After first discount of 25%, price = 1.8 × CP × 0.75 = 1.35 × CP. Step 3: After second discount of 15%, price = 1.35 × CP × 0.85 = 1.1475 × CP. Step 4: Given final price = ₹918, so 1.1475 × CP = 918. Step 5: CP = 918 ÷ 1.1475 = 800. Therefore, cost price is ₹800.

Question 10

A shopkeeper marks up goods by 80% above cost price. He then offers two successive discounts of 25% and 20% on the marked price. If the final selling price is ₹432, what is the cost price?

Accepted Answer

Step 1: Let CP = x. Then MP = x + 0.80x = 1.80x. Step 2: After first discount of 25%, price = 1.80x × 0.75 = 1.35x. Step 3: After second discount of 20%, price = 1.35x × 0.80 = 1.08x. Step 4: Given 1.08x = 432, so x = 400. Therefore, cost price is ₹400.

Question 11

A merchant offers a discount of 10% on the marked price of a shirt. If the customer pays ₹540 after the discount, what was the marked price?

Accepted Answer

Step 1: Let Marked Price = MP. Step 2: After 10% discount, customer pays 90% of MP. Step 3: 90% of MP = ₹540. Step 4: (90/100) × MP = 540. Step 5: MP = 540 × (100/90) = 540 × (10/9) = ₹600.

Question 12

A retailer marks up the cost price by 60% and then offers a discount of 25% on the marked price. What is his profit percentage?

Accepted Answer

Step 1: Let Cost Price (CP) = ₹100. Step 2: Marked Price (MP) = CP + 60% of CP = 100 + 60 = ₹160. Step 3: Discount = 25% of MP = (25/100) × 160 = ₹40. Step 4: Selling Price (SP) = MP − Discount = 160 − 40 = ₹120. Step 5: Profit = SP − CP = 120 − 100 = ₹20. Step 6: Profit% = (Profit/CP) × 100 = (20/100) × 100 = 20%.

Question 13

A merchant sells an item at ₹1200 after giving a discount of 25% on the marked price. What is the marked price?

Accepted Answer

Step 1: Selling Price (SP) = ₹1200. Step 2: Discount = 25%, so SP = MP × (1 − 25/100) = MP × 0.75. Step 3: 1200 = MP × 0.75. Step 4: MP = 1200 ÷ 0.75 = ₹1600.

Question 14

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 MP = 20% of 500 = ₹100. Step 3: Selling Price (SP) = MP − Discount = 500 − 100 = ₹400. Therefore, the selling price is ₹400.

Question 15

The marked price of a shirt is ₹1000. A customer gets two successive discounts of 10% and 15%. What is the final selling price?

Accepted Answer

Step 1: Marked Price (MP) = ₹1000. Step 2: After first discount of 10%: Price = 1000 × (1 − 10/100) = 1000 × 0.9 = ₹900. Step 3: After second discount of 15% on ₹900: Price = 900 × (1 − 15/100) = 900 × 0.85 = ₹765.

Question 16

The selling price of an item is ₹750 after a discount of 25% on the marked price. What is the marked price?

Accepted Answer

Step 1: Selling Price (SP) = ₹750, Discount = 25%. Step 2: If discount is 25%, then SP = MP × (1 − 25/100) = MP × 0.75. Step 3: Therefore, 750 = MP × 0.75, so MP = 750 / 0.75 = ₹1000. The marked price is ₹1000.

Question 17

If the selling price of an item is ₹450 and the discount given is 10%, what is the marked price?

Accepted Answer

Step 1: Let Marked Price = MP. Step 2: Discount = 10%, so SP = 90% of MP. Step 3: 450 = 0.90 × MP. Step 4: MP = 450 ÷ 0.90 = ₹500. Therefore, the marked price is ₹500.

Question 18

If the marked price of a book is ₹800 and it is sold at ₹600, what is the discount percentage?

Accepted Answer

Step 1: Marked Price (MP) = ₹800, Selling Price (SP) = ₹600. Step 2: Discount = MP − SP = 800 − 600 = ₹200. Step 3: Discount% = (Discount / MP) × 100 = (200 / 800) × 100 = 25%. Therefore, the discount percentage is 25%.

Question 19

An article costs ₹400 to the shopkeeper. He marks it up by 50% and then offers a discount of 20%. What is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹400. Step 2: Marked Price (MP) = CP + 50% of CP = 400 + (50/100 × 400) = 400 + 200 = ₹600. Step 3: Selling Price (SP) = MP − 20% of MP = 600 − (20/100 × 600) = 600 − 120 = ₹480. Step 4: Profit = SP − CP = 480 − 400 = ₹80. Step 5: Profit% = (Profit / CP) × 100 = (80 / 400) × 100 = 20%. Therefore, the profit percentage is 20%.

Question 20

A shopkeeper marks an article at ₹800. He gives a discount of 15% on the marked price. What is the selling price?

Accepted Answer

Step 1: Marked Price (MP) = ₹800. Step 2: Discount = 15% of ₹800 = 0.15 × 800 = ₹120. Step 3: Selling Price (SP) = MP − Discount = 800 − 120 = ₹680. Therefore, the selling price is ₹680.

Question 21

A merchant offers two successive discounts of 20% and 10% on an article marked at ₹1000. What is the final selling price?

Accepted Answer

Step 1: Marked Price = ₹1000. Step 2: After first discount of 20%: Price = 1000 × (1 − 0.20) = 1000 × 0.80 = ₹800. Step 3: After second discount of 10% on ₹800: Price = 800 × (1 − 0.10) = 800 × 0.90 = ₹720. Therefore, the final selling price is ₹720.

Question 22

The marked price of a book is ₹250. After giving a discount of 12%, the shopkeeper still makes a profit of 20% on the cost price. What is the cost price of the book?

Accepted Answer

Step 1: Marked Price (MP) = ₹250. Step 2: Discount = 12%, so SP = 250 × 0.88 = ₹220. Step 3: Profit = 20%, meaning SP = 1.20 × CP. Step 4: 220 = 1.20 × CP. Step 5: CP = 220 ÷ 1.20 = ₹183.33. For verification: Cost price is ₹183.33 (or 550/3 rupees exactly).

Question 23

A trader marks his goods 40% above the cost price and gives a discount of 10% on the marked price. If the cost price is ₹600, what is the profit made?

Accepted Answer

Step 1: Cost Price (CP) = ₹600. Step 2: Markup = 40%, so MP = 600 × (1 + 40/100) = 600 × 1.4 = ₹840. Step 3: Discount = 10% of MP = 10% of 840 = ₹84. Step 4: Selling Price (SP) = 840 − 84 = ₹756. Step 5: Profit = SP − CP = 756 − 600 = ₹156.

Question 24

A store gives successive discounts of 10% and 20% on an article marked at ₹2000. What is the final selling price?

Accepted Answer

Step 1: Marked Price (MP) = ₹2000. Step 2: After first discount of 10%: Price = 2000 × (1 − 10/100) = 2000 × 0.9 = ₹1800. Step 3: After second discount of 20% on ₹1800: Price = 1800 × (1 − 20/100) = 1800 × 0.8 = ₹1440. Therefore, the final selling price is ₹1440.

Question 25

A merchant offers a discount of 15% on the marked price of ₹1200. What amount does the customer pay?

Accepted Answer

Step 1: Marked Price (MP) = ₹1200, Discount = 15%. Step 2: Discount amount = 15% of 1200 = (15/100) × 1200 = ₹180. Step 3: Selling Price (SP) = MP − Discount = 1200 − 180 = ₹1020. Therefore, the customer pays ₹1020.

Question 26

The marked price of a book is ₹500. After giving a discount of 20%, the shopkeeper still makes a profit of 25% on the cost price. What is the cost price of the book?

Accepted Answer

Step 1: Marked Price (MP) = ₹500. Step 2: Discount = 20% of 500 = ₹100. Step 3: Selling Price (SP) = 500 − 100 = ₹400. Step 4: Profit = 25%, so SP = CP × (1 + 25/100) = CP × 1.25. Step 5: 400 = CP × 1.25, therefore CP = 400 ÷ 1.25 = ₹320.

Question 27

A shopkeeper marks an article at ₹800. He gives a discount of 15% on the marked price. What is the selling price?

Accepted Answer

Step 1: Marked Price (MP) = ₹800. Step 2: Discount = 15% of ₹800 = (15/100) × 800 = ₹120. Step 3: Selling Price (SP) = MP − Discount = 800 − 120 = ₹680.

Question 28

A retailer buys an item for ₹400 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) = ₹400. Step 2: Markup = 50%, so MP = 400 × (1 + 50/100) = 400 × 1.5 = ₹600. Step 3: Discount = 20% of MP = 20% of 600 = ₹120. Step 4: Selling Price (SP) = 600 − 120 = ₹480. Step 5: Profit = SP − CP = 480 − 400 = ₹80. Step 6: Profit% = (80/400) × 100 = 20%.

Question 29

A merchant offers two successive discounts of 10% and 15% on an article marked at ₹5,000. A customer also has a coupon for an additional 5% discount on the final price. What is the final selling price?

Accepted Answer

Step 1: Apply first discount of 10%: Price after 1st discount = 5,000 × 0.90 = ₹4,500. Step 2: Apply second discount of 15%: Price after 2nd discount = 4,500 × 0.85 = ₹3,825. Step 3: Apply coupon discount of 5%: Final SP = 3,825 × 0.95 = ₹3,633.75. However, checking for clean answer: 5,000 × 0.90 × 0.85 × 0.95 = 5,000 × 0.72675 = ₹3,633.75. Rounding to nearest rupee: ₹3,634.

Question 30

A shopkeeper marks an article 60% above its cost price. He then gives a discount of 25% on the marked price. If the cost price is ₹400, what is the selling price?

Accepted Answer

Step 1: Calculate marked price with 60% markup: MP = 400 × (100 + 60)/100 = 400 × 1.60 = ₹640. Step 2: Calculate selling price after 25% discount on MP: SP = 640 × (100 - 25)/100 = 640 × 0.75 = ₹480.

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