Question 1

A shopkeeper buys an article at ₹500. He marks it up by 40% and then gives a discount of 10% on the marked price. Later, he offers a further discount of 5% on the new selling price. What is his overall profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹500. Step 2: Marked Price (MP) = 500 + 40% of 500 = 500 + 200 = ₹700. Step 3: After first discount of 10%: Selling Price₁ = 700 − 10% of 700 = 700 − 70 = ₹630. Step 4: After second discount of 5% on ₹630: Selling Price₂ = 630 − 5% of 630 = 630 − 31.50 = ₹598.50. Step 5: Profit = 598.50 − 500 = ₹98.50. Step 6: Profit% = (98.50 / 500) × 100 = 19.7%. Therefore, the overall profit percentage is 19.7%.

Question 2

A merchant sells an item at a loss of 10%, and then buys it back and sells it again at a loss of 20%. If the original cost price was ₹1000, what is the net loss percentage?

Accepted Answer

Step 1: First sale — Cost Price = ₹1000, Loss = 10%. Selling Price = 1000 − (10% of 1000) = 1000 − 100 = ₹900. Step 2: Second transaction — He buys at ₹900 (the previous selling price becomes the new cost price), Loss = 20%. Selling Price = 900 − (20% of 900) = 900 − 180 = ₹720. Step 3: Net loss = 1000 − 720 = ₹280. Net loss % = (280/1000) × 100 = 28%.

Question 3

A trader buys an article and sells it at a profit of 20%. If he had bought it at 10% less and sold it for ₹6 more, he would have gained 40%. Find the cost price of the article.

Accepted Answer

Step 1: Let original CP = ₹x. Original SP = 1.2x. Step 2: New CP = 0.9x, New SP = 1.2x + 6. New profit = 40%, so New SP = 1.4 × 0.9x = 1.26x. Step 3: 1.26x = 1.2x + 6 → 0.06x = 6 → x = ₹100. Therefore, the cost price is ₹100.

Question 4

A shopkeeper bought a watch for ₹800. He marked it at 40% above the cost price and offered a discount of 10% on the marked price. What is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹800. Step 2: Marked Price (MP) = 800 + (40% of 800) = 800 + 320 = ₹1120. Step 3: Discount = 10% of 1120 = ₹112. Step 4: Selling Price (SP) = 1120 - 112 = ₹1008. Step 5: Profit = SP - CP = 1008 - 800 = ₹208. Step 6: Profit% = (208/800) × 100 = 26%. Therefore, the answer is 26%.

Question 5

A dishonest shopkeeper claims to sell goods at cost price, but uses a false weight of 900 g instead of 1 kg. What is his profit percentage?

Accepted Answer

Step 1: The shopkeeper gives only 900 g but charges for 1000 g (1 kg). Step 2: If cost price per gram is C, then Cost Price for 900 g = 900C, but Selling Price (charged for 1000 g) = 1000C. Step 3: Profit = SP − CP = 1000C − 900C = 100C. Step 4: Profit % = (Profit / CP) × 100 = (100C / 900C) × 100 = (100/900) × 100 = 11.11% (or 11⅑%).

Question 6

A shopkeeper marks an item 40% above cost price. He then offers a discount of 20% on the marked price. If the cost price is ₹250, what is the selling price?

Accepted Answer

Step 1: CP = ₹250. Step 2: MP = 250 + (40% of 250) = 250 + 100 = ₹350. Step 3: Discount = 20% of 350 = 0.20 × 350 = ₹70. Step 4: SP = 350 − 70 = ₹280. Therefore, the selling price is ₹280.

Question 7

A shopkeeper buys an item at ₹500. He makes a profit of 20% on the first sale, and then sells the item again at a profit of 25% on the new cost price. What is his overall profit percentage?

Accepted Answer

Step 1: First sale — Cost Price = ₹500, Profit = 20%. Selling Price = 500 + (20% of 500) = 500 + 100 = ₹600. Step 2: Second sale — New Cost Price = ₹600, Profit = 25%. Selling Price = 600 + (25% of 600) = 600 + 150 = ₹750. Step 3: Overall profit = 750 − 500 = ₹250. Overall profit % = (250/500) × 100 = 50%.

Question 8

A shopkeeper marks an item at ₹1200 and gives a discount of 10%. He then sells this discounted item at a further loss of 5% in a clearance sale. What is his overall loss or profit percentage from the marked price?

Accepted Answer

Step 1: Marked Price = ₹1200. After 10% discount: Selling Price₁ = 1200 − (10% of 1200) = 1200 − 120 = ₹1080. Step 2: In clearance sale, he sells at 5% loss on ₹1080: Selling Price₂ = 1080 − (5% of 1080) = 1080 − 54 = ₹1026. Step 3: Assuming marked price equals cost price (₹1200), net loss = 1200 − 1026 = ₹174. Net loss % = (174/1200) × 100 = 14.5%.

Question 9

A trader buys goods at ₹80 per unit. He sells 60% of the stock at 25% profit and the remaining 40% at 10% loss. What is his overall profit or loss percentage?

Accepted Answer

Step 1: CP per unit = ₹80. Step 2: For 60% stock at 25% profit: SP = 80 × 1.25 = ₹100 per unit. Profit on 60 units = 60 × (100 − 80) = ₹1200. Step 3: For 40% stock at 10% loss: SP = 80 × 0.90 = ₹72 per unit. Loss on 40 units = 40 × (80 − 72) = ₹320. Step 4: Net profit = 1200 − 320 = ₹880. Step 5: Total CP = 100 × 80 = ₹8000. Step 6: Overall profit % = (880/8000) × 100 = 11%. Therefore, the answer is 11% profit.

Question 10

A shopkeeper buys an item at ₹500. He marks it up by 20% and then offers a discount of 10% on the marked price. Later, he sells the remaining stock at a further discount of 5% on the already discounted price. What is his overall profit percentage on the item?

Accepted Answer

Step 1: Cost Price (CP) = ₹500. Step 2: Marked Price (MP) = 500 + 20% of 500 = 500 + 100 = ₹600. Step 3: After first discount of 10%: Price = 600 - 10% of 600 = 600 - 60 = ₹540. Step 4: After second discount of 5% on ₹540: Final Selling Price (SP) = 540 - 5% of 540 = 540 - 27 = ₹513. Step 5: Profit = SP - CP = 513 - 500 = ₹13. Step 6: Profit % = (13/500) × 100 = 2.6%. Therefore, the overall profit percentage is 2.6%.

Question 11

A trader buys goods at ₹2000 and sells them at a profit of 15%. He then buys the same goods again at the selling price and sells them at a loss of 10%. What is his net profit or loss percentage over both transactions?

Accepted Answer

Step 1: First transaction — Cost Price = ₹2000, Profit = 15%. Selling Price = 2000 + (15% of 2000) = 2000 + 300 = ₹2300. Step 2: Second transaction — Cost Price = ₹2300 (previous selling price), Loss = 10%. Selling Price = 2300 − (10% of 2300) = 2300 − 230 = ₹2070. Step 3: Net profit = 2070 − 2000 = ₹70. Net profit % = (70/2000) × 100 = 3.5%.

Question 12

A shopkeeper buys an item at ₹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 13

A merchant sells an item at a loss of 15%. If he had sold it for ₹100 more, he would have made a profit of 5%. What is the cost price of the item?

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 = 100, so 1.05x − 0.85x = 100. Step 5: 0.20x = 100, therefore x = 500. The cost price is ₹500.

Question 14

A person buys a laptop for ₹40,000. He sells it at a 20% profit. The buyer then sells it at a 15% loss. What is the final selling price?

Accepted Answer

Step 1: Original CP = ₹40,000. Step 2: First seller's SP = 40,000 × 1.20 = ₹48,000 (this becomes the second buyer's CP). Step 3: Second seller's SP = 48,000 × 0.85 = ₹40,800. Therefore, the final selling price is ₹40,800.

Question 15

A dealer uses 1200 g weights instead of 1 kg while buying from farmers, and uses 800 g weights instead of 1 kg while selling to customers. If he claims to sell at the same rate per gram as he buys, what is his profit percentage?

Accepted Answer

Step 1: While buying, dealer uses 1200g weights (gets 1200g but pays for 1000g). Cost per gram = C. Cost for 1200g = 1000C. Step 2: While selling, dealer uses 800g weights (gives 800g but charges for 1000g). Revenue for 800g = 1000C. Step 3: Effective cost per gram = 1000C / 1200g = 5C/6. Effective selling price per gram = 1000C / 800g = 5C/4. Step 4: Profit per gram = 5C/4 - 5C/6 = (15C - 10C)/12 = 5C/12. Step 5: Profit % = [(5C/12) / (5C/6)] × 100 = [(5C/12) × (6/5C)] × 100 = (6/12) × 100 = 50%.

Question 16

A shopkeeper uses 950 g weights instead of 1 kg while selling. If he claims to sell at cost price, what is his profit percentage?

Accepted Answer

Step 1: The shopkeeper gives 950 g but charges for 1000 g. Step 2: If cost price per gram is C, then cost to shopkeeper for 950g = 950C. Step 3: Selling price charged = 1000C. Step 4: Profit = 1000C - 950C = 50C. Step 5: Profit % = (50C / 950C) × 100 = (50/950) × 100 = 5.26% ≈ 5⁵⁄₁₉%.

Question 17

A shopkeeper buys a watch for ₹800 and marks it at a price such that after giving a discount of 20%, he still makes a profit of 25%. At what price is the watch marked?

Accepted Answer

Step 1: Let the marked price be M. Step 2: After 20% discount, selling price = M × (80/100) = 0.8M. Step 3: For 25% profit on cost price ₹800, selling price = 800 × (125/100) = ₹1000. Step 4: Therefore, 0.8M = 1000, so M = 1000 ÷ 0.8 = ₹1250.

Question 18

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 19

A dishonest shopkeeper claims to sell goods at cost price, but uses false weights. He gives 900 g instead of 1 kg. What is his profit percentage?

Accepted Answer

Step 1: The shopkeeper claims to sell at cost price, meaning selling price = cost price per unit weight.

Step 2: He uses false weights — gives 900 g when customer pays for 1000 g.

Step 3: Let's say cost price per gram = ₹1 (for simplicity).

Step 4: Cost Price (CP) of 900 g = ₹900.

Step 5: Selling Price (SP) = Price for 1000 g = ₹1000 (since he claims to sell at CP of 1000 g).

Step 6: Profit = SP - CP = 1000 - 900 = ₹100.

Step 7: Profit % = (Profit/CP) × 100 = (100/900) × 100 = 100/9 = 11.11% ≈ 11.11%

Alternatively, using formula: Profit % = [(True Weight - False Weight)/False Weight] × 100 = [(1000 - 900)/900] × 100 = (100/900) × 100 = 11⅑% or 11.11%

Therefore, the profit percentage is 11.11% (or 11⅑%).

Question 20

A vendor buys oranges at ₹5 per dozen. He sells them at ₹0.50 per orange. What is his profit percentage?

Accepted Answer

Step 1: CP per dozen = ₹5. Step 2: Number of oranges per dozen = 12. Step 3: CP per orange = 5/12 ≈ ₹0.417. Step 4: SP per orange = ₹0.50. Step 5: Profit per orange = 0.50 − 0.417 = ₹0.083. Step 6: Profit % = (0.083/0.417) × 100 = (0.50 − 5/12)/(5/12) × 100 = (6/12 − 5/12)/(5/12) × 100 = (1/12)/(5/12) × 100 = (1/5) × 100 = 20%. Therefore, the profit percentage is 20%.

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