Question 1

A shopkeeper marks his goods 25% above the cost price and offers a discount of 10%. What is his profit percentage?

Accepted Answer

Step 1: Let Cost Price (CP) = ₹100. Step 2: Marked Price (MP) = 100 + 25% of 100 = ₹125. Step 3: Selling Price (SP) after 10% discount = 125 − 10% of 125 = 125 − 12.50 = ₹112.50. Step 4: Profit = SP − CP = 112.50 − 100 = ₹12.50. Step 5: Profit% = (12.50/100) × 100 = 12.5%. Therefore, the profit percentage is 12.5%.

Question 2

A shopkeeper marks an article at ₹1,200. He offers a discount of 15% on the marked price. However, he still makes a profit of 20% on the cost price. What is the cost price of the article?

Accepted Answer

Step 1: Calculate Selling Price (SP) after 15% discount on MP of ₹1,200.
Discount = 15% of 1,200 = 0.15 × 1,200 = ₹180
SP = MP − Discount = 1,200 − 180 = ₹1,020

Step 2: Use Profit formula to find Cost Price (CP).
Profit = 20% means SP = CP × (1 + 20/100) = CP × 1.20
1,020 = CP × 1.20
CP = 1,020 ÷ 1.20 = ₹850

Step 3: Verify: Profit = SP − CP = 1,020 − 850 = ₹170
Profit% = (170/850) × 100 = 20% ✓

Therefore, the cost price is ₹850.

Question 3

A shopkeeper marks his goods 40% above cost price and offers a discount of 20% on the marked price. He also gives one article free on purchase of every 4 articles. Find the overall profit or loss percentage.

Accepted Answer

Step 1: Let CP of each article = 100. So CP of 4 articles = 400. Step 2: MP of each article = 140 (40% above CP). MP of 4 articles = 560. Step 3: After 20% discount on MP: SP of 4 articles = 560 × 0.80 = 448. Step 4: But customer gets 5 articles (4 + 1 free), so actual CP = 5 × 100 = 500. Step 5: Profit/Loss% = (448 - 500)/500 × 100 = -52/500 × 100 = -10.4%. Therefore, the shopkeeper incurs a loss of 10.4%.

Question 4

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: Let Marked Price (MP) = x. Step 2: Discount = 25% of MP = 0.25x. Step 3: Selling Price (SP) = MP − Discount = x − 0.25x = 0.75x. Step 4: Given SP = ₹450, so 0.75x = 450. Step 5: x = 450/0.75 = ₹600. Therefore, the marked price is ₹600.

Question 5

A retailer buys a product for ₹300 and marks it up by 50%. He then gives 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 CP = 0.5 × 300 = ₹150. Step 3: Marked Price (MP) = CP + Markup = 300 + 150 = ₹450. Step 4: Discount = 20% of MP = 0.2 × 450 = ₹90. Step 5: Selling Price (SP) = MP − Discount = 450 − 90 = ₹360. Step 6: Profit = SP − CP = 360 − 300 = ₹60. Step 7: Profit% = (Profit/CP) × 100 = (60/300) × 100 = 20%. Therefore, the profit percentage is 20%.

Question 6

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

Question 7

A retailer buys a shirt for ₹240 and marks it up by 50%. He then gives a discount of 10% on the marked price. What is his profit percentage?

Accepted Answer

Step 1: CP = ₹240. Step 2: MP = CP + 50% of CP = 240 + (50/100 × 240) = 240 + 120 = ₹360. Step 3: SP = MP − 10% of MP = 360 − (10/100 × 360) = 360 − 36 = ₹324. Step 4: Profit = SP − CP = 324 − 240 = ₹84. Step 5: Profit% = (84/240) × 100 = 35%.

Question 8

A discount of 30% is given on the marked price of ₹1200. What is the discount amount in rupees?

Accepted Answer

Step 1: Marked Price (MP) = ₹1200. Step 2: Discount% = 30%. Step 3: Discount Amount = 30% of MP = (30/100) × 1200 = 0.30 × 1200 = ₹360. Therefore, the discount amount is ₹360.

Question 9

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: MP = ₹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.

Question 10

If the cost price of an item is ₹200 and it is sold at a loss of 10%, what is the selling price?

Accepted Answer

Step 1: Cost Price (CP) = ₹200. Step 2: Loss = 10% of CP = 10% of 200 = ₹20. Step 3: Selling Price (SP) = CP − Loss = 200 − 20 = ₹180. Therefore, the selling price is ₹180.

Question 11

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

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 12

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 13

A merchant offers two successive discounts of 15% and 10% on the marked price of an item. If the final selling price is ₹3,060, what is the marked price?

Accepted Answer

Step 1: When two successive discounts are given, the combined effect is: Final Price = MP × (1 - d₁) × (1 - d₂) = MP × 0.85 × 0.90. Step 2: Calculate: 3,060 = MP × 0.765. Step 3: MP = 3,060 / 0.765 = ₹4,000.

Question 14

A shopkeeper marks a product at ₹2,500. He offers a discount of 20% on the marked price. If his cost price is ₹1,600, what is his profit percentage?

Accepted Answer

Step 1: Calculate selling price after 20% discount on MP of ₹2,500. SP = 2,500 × (1 - 0.20) = 2,500 × 0.80 = ₹2,000. Step 2: Calculate profit using formula: Profit = SP - CP = 2,000 - 1,600 = ₹400. Step 3: Profit % = (Profit / CP) × 100 = (400 / 1,600) × 100 = 25%.

Question 15

A store sells an item at ₹1,800 after giving a discount of 25% on the marked price. The store earns a profit of 50% on the cost price. What is the cost price of the item?

Accepted Answer

Step 1: Use discount formula to find MP. If SP = ₹1,800 and discount = 25%, then SP = MP × (1 - 0.25), so 1,800 = MP × 0.75. Therefore, MP = 1,800 / 0.75 = ₹2,400. Step 2: Use profit formula to find CP. If profit = 50%, then SP = CP × (1 + 0.50), so 1,800 = CP × 1.50. Therefore, CP = 1,800 / 1.50 = ₹1,200.

Question 16

A trader marks goods 50% above cost price and gives a discount of 20% on the marked price. Later, he gives an additional discount of 10% on the already discounted price. What is his overall profit or loss percentage?

Accepted Answer

Step 1: Let Cost Price (CP) = ₹100. Step 2: Marked Price (MP) = 100 + 50% of 100 = ₹150. Step 3: After first discount of 20%: Price = 150 × 0.80 = ₹120. Step 4: After second discount of 10%: Final Selling Price (SP) = 120 × 0.90 = ₹108. Step 5: Profit = SP - CP = 108 - 100 = ₹8. Step 6: Profit % = (8/100) × 100 = 8%.

Question 17

A shopkeeper marks an article at ₹800. He offers a discount of 15% on the marked price. If he still makes a profit of 25% on the cost price, what is the cost price of the article?

Accepted Answer

Step 1: Marked Price (MP) = ₹800. Step 2: Discount = 15% of 800 = ₹120. Step 3: Selling Price (SP) = 800 - 120 = ₹680. Step 4: Profit = 25%, so SP = CP × (1 + 0.25) = 1.25 × CP. Step 5: 680 = 1.25 × CP, therefore CP = 680 ÷ 1.25 = ₹544.

Question 18

A retailer buys goods at ₹3,000 per unit. He wants to earn a profit of 40% after giving a discount of 20% on the marked price. What should be the marked price per unit?

Accepted Answer

Step 1: Calculate desired selling price using profit formula. If profit = 40%, then SP = CP × (1 + 0.40) = 3,000 × 1.40 = ₹4,200. Step 2: Use discount formula to find MP. If discount = 20%, then SP = MP × (1 - 0.20), so 4,200 = MP × 0.80. Step 3: MP = 4,200 / 0.80 = ₹5,250.

Question 19

A retailer buys goods at ₹2000 per unit. He marks them up by 40% and then gives a discount of 20% on the marked price. What is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹2000. Step 2: Marked Price (MP) = CP + 40% of CP = 2000 × 1.40 = ₹2800. Step 3: Discount = 20% of MP = 0.20 × 2800 = ₹560. Step 4: Selling Price (SP) = 2800 - 560 = ₹2240. Step 5: Profit = SP - CP = 2240 - 2000 = ₹240. Step 6: Profit % = (240/2000) × 100 = 12%.

Question 20

A merchant offers two successive discounts of 10% and 15% on an article marked at ₹5000. 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: Marked Price (MP) = ₹5000. Step 2: After first discount of 10%: Price = 5000 × 0.90 = ₹4500. Step 3: After second discount of 15%: Price = 4500 × 0.85 = ₹3825. Step 4: After coupon discount of 5%: Final Price = 3825 × 0.95 = ₹3633.75. Step 5: Rounding to nearest rupee: ₹3634.

Question 21

A shopkeeper buys an item for ₹1200 and wants to earn a profit of 30%. He marks the item at a price such that after giving a discount of 12%, he still achieves his target profit. What is the marked price?

Accepted Answer

Step 1: Cost Price (CP) = ₹1200. Step 2: Target Profit = 30%, so Selling Price (SP) = 1200 × 1.30 = ₹1560. Step 3: Let Marked Price = MP. After 12% discount: SP = MP × (1 - 0.12) = MP × 0.88. Step 4: 1560 = MP × 0.88, therefore MP = 1560 ÷ 0.88 = ₹1772.73 ≈ ₹1773.

Question 22

An article is marked at 60% above its cost price. A discount of 25% is given on the marked price. If the selling price is ₹2880, what is the cost price?

Accepted Answer

Step 1: Let Cost Price (CP) = x. Step 2: Marked Price (MP) = x + 60% of x = 1.60x. Step 3: Discount = 25% of MP = 0.25 × 1.60x = 0.40x. Step 4: Selling Price (SP) = MP - Discount = 1.60x - 0.40x = 1.20x. Step 5: Given SP = ₹2880, so 1.20x = 2880, therefore x = 2880 ÷ 1.20 = ₹2400.

Question 23

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.

SSC CHSL Discount & MP

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