Question 1

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 2

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 3

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 4

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 5

A fraudulent dealer buys goods at ₹10 per kg and sells at ₹12 per kg, but uses 800 g weights instead of 1 kg. What is his overall profit percentage?

Accepted Answer

Step 1: Cost Price for 1000 g = ₹10. Cost Price per gram = ₹10/1000 = ₹0.01. Step 2: Selling Price for 800 g (which he claims is 1 kg) = ₹12. Step 3: Actual Cost Price for 800 g = 800 × 0.01 = ₹8. Step 4: Profit = ₹12 - ₹8 = ₹4. Step 5: Profit % = (4/8) × 100 = 50%.

Question 6

A dealer claims to sell sugar at cost price but uses 750 g weights instead of 1 kg. A customer buys 3 kg of sugar (as per dealer's weights). How much actual sugar does the customer get?

Accepted Answer

Step 1: Customer asks for 3 kg as per dealer's weights. Step 2: Dealer's 1 kg = 750 g actual. Step 3: Dealer's 3 kg = 3 × 750 = 2250 g actual. Step 4: Customer gets 2250 g = 2.25 kg actual sugar.

Question 7

A dishonest shopkeeper claims to sell goods at cost price, but uses a faulty weight machine. When he should give 1000 g, he actually gives only 800 g. What is his profit percentage?

Accepted Answer

Step 1: The shopkeeper claims to sell at cost price, meaning he charges the customer for 1000 g at cost price per gram. Step 2: However, he only gives 800 g. So for every 1000 g of payment received, he gives away only 800 g of goods. Step 3: His cost for 800 g = 800 × (CP per gram). His revenue = 1000 × (CP per gram). Step 4: Profit = Revenue − Cost = 1000 × CP − 800 × CP = 200 × CP. Step 5: Profit % = (Profit / Cost) × 100 = (200 × CP / 800 × CP) × 100 = (200/800) × 100 = 25%. Therefore, the answer is 25%.

Question 8

A shopkeeper buys sugar at ₹20 per kg. He uses 750 g weights instead of 1 kg and also marks up the price to ₹25 per kg. What is his profit percentage?

Accepted Answer

Step 1: Cost Price for 1000 g = ₹20. Cost Price for 750 g = (750/1000) × 20 = ₹15. Step 2: Selling Price for 750 g (which he claims is 1 kg) = ₹25. Step 3: Profit = ₹25 - ₹15 = ₹10. Step 4: Profit % = (10/15) × 100 = 66.67%.

Question 9

A merchant uses 800 g weights instead of 1 kg and sells at 25% profit on cost price. What is the effective profit percentage?

Accepted Answer

Step 1: Let CP per gram = ₹1. CP of 800 g = ₹800. Step 2: Merchant marks 800 g as 1000 g and sells at 25% profit on CP. Step 3: SP of 800 g = 1000 × 1.25 = ₹1250. Step 4: Effective Profit % = [(1250 - 800)/800] × 100 = (450/800) × 100 = 56.25%.

Question 10

A shopkeeper uses 1200 g weights instead of 1 kg while buying and 800 g weights instead of 1 kg while selling. If he buys and sells at the same marked price per kg, what is his profit percentage?

Accepted Answer

Step 1: Let marked price = ₹1 per gram. Step 2: While buying: He pays for 1000 g but receives 1200 g. Cost of 1200 g = ₹1000. Step 3: While selling: He gives 800 g but charges for 1000 g. Revenue from 800 g = ₹1000. Step 4: For 1200 g bought, he can sell 1200/800 = 1.5 batches. Revenue = 1.5 × 1000 = ₹1500. Step 5: Profit % = [(1500 - 1000)/1000] × 100 = 50%.

Question 11

A fraudulent dealer buys goods at ₹10 per kg and uses weights such that he gives only 960 g for every 1 kg sold. If he wants an overall profit of 20%, at what price per kg should he sell?

Accepted Answer

Step 1: CP per kg = ₹10. For every 1 kg sold, he gives 960 g. Step 2: Actual cost of 960 g = 960/1000 × 10 = ₹9.60. Step 3: For 20% profit on actual cost: SP = 9.60 × 1.20 = ₹11.52 per kg (declared).

Question 12

A merchant buys rice at ₹40 per kg. He uses false weights and gives only 800 g for every 1 kg sold. He also offers a 10% discount on the marked price. If his marked price is ₹50 per kg, what is his profit or loss percentage?

Accepted Answer

Step 1: CP per kg = ₹40. For 1 kg sold, he gives 800 g. Actual CP of 800 g = (800/1000) × 40 = ₹32. Step 2: Marked price = ₹50 per kg. Discount = 10%. SP per kg = 50 × 0.90 = ₹45. Step 3: Profit per kg = 45 - 32 = ₹13. Step 4: Profit % = (13/32) × 100 = 40.625% ≈ 40.63%.

Question 13

A dishonest grocer claims to sell sugar at ₹50 per kg but uses false weights. A customer who buys what the grocer claims is 2 kg actually receives only 1.6 kg. If the grocer's cost price is ₹40 per kg, what is the actual profit percentage?

Accepted Answer

Step 1: Customer pays for 2 kg at ₹50/kg = ₹100 (SP). Step 2: Customer actually receives 1.6 kg. Step 3: CP for 1.6 kg = 1.6 × 40 = ₹64. Step 4: Profit = 100 - 64 = ₹36. Step 5: Profit % = (36/64) × 100 = 56.25%.

Question 14

A dealer uses 800 g weight instead of 1 kg and sells at 25% profit on cost price. A customer buys goods worth ₹1000 at marked price. How much less does the customer actually pay in terms of quantity compared to what he should have received?

Accepted Answer

Step 1: Customer pays ₹1000 for goods marked as 1 kg (1000 g). Step 2: Due to false weight (800 g), customer receives only 800 g. Step 3: Actual quantity should be: If 800 g costs ₹1000 at 25% markup, then CP of 800 g = 1000/1.25 = ₹800. Step 4: CP per gram = 800/800 = ₹1 per gram. Step 5: For ₹1000, customer should receive 1000 g, but receives 800 g. Step 6: Shortfall = 1000 - 800 = 200 g.

Question 15

A dealer buys goods at ₹60 per kg and sells at ₹75 per kg. However, he uses a faulty balance that shows 1 kg when the actual weight is 1.2 kg. What is his actual profit percentage?

Accepted Answer

Step 1: The balance shows 1 kg but actual weight is 1.2 kg. Step 2: For every transaction, the dealer gives 1.2 kg but charges for 1 kg. Step 3: CP for 1.2 kg = 1.2 × 60 = ₹72. Step 4: SP for 1.2 kg (charged as 1 kg) = 1 × 75 = ₹75. Step 5: Profit = 75 - 72 = ₹3. Step 6: Profit % = (3/72) × 100 = 4.166...% ≈ 4⅙%.

Question 16

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 actual profit percentage?

Accepted Answer

Step 1: The shopkeeper gives 900 g but charges for 1000 g. Step 2: Cost Price for 900 g = 900 units. Selling Price for 900 g = 1000 units (charged as 1 kg). Step 3: Profit = SP - CP = 1000 - 900 = 100 units. Step 4: Profit % = (100/900) × 100 = 11.11% ≈ 11⅑%.

Question 17

A fraudulent dealer sells goods at 20% profit but uses weights such that 1200 g is marked as 1 kg. What is his actual profit percentage?

Accepted Answer

Step 1: False weight: 1200 g marked as 1000 g. Step 2: Let CP per gram = ₹1. Cost of 1200 g = ₹1200. Step 3: He charges for 1000 g at 20% profit = 1000 × 1.20 = ₹1200. Step 4: Actual SP for 1200 g = ₹1200. Step 5: Profit % = (1200 - 1200)/1200 × 100 = 0%. This is a trap question — he makes NO profit despite claiming 20% profit due to false weights working against him.

Question 18

A fraudulent dealer sells goods at 25% profit but uses weights such that 1200 g is sold as 1 kg. What is the actual profit percentage earned by the dealer?

Accepted Answer

Step 1: The dealer uses 1200 g but charges for 1000 g. Step 2: Let CP per gram = ₹1. Then CP for 1200 g = ₹1200. Step 3: SP for 1000 g at 25% profit = 1000 × 1.25 = ₹1250. Step 4: Actual profit = 1250 - 1200 = ₹50. Step 5: Actual profit % = (50/1200) × 100 = 4.166...% ≈ 4⅙%.

Question 19

A dishonest grocer uses a false weight of 950 g for 1 kg and also adulterates the goods such that the cost price is effectively reduced by 10%. If he sells at the marked price (which is 20% above the original cost price), what is his profit percentage?

Accepted Answer

Step 1: Original CP per gram = Re. 1. For 1000 g, original CP = Rs. 1000. Step 2: After adulteration, effective CP = 1000 × 0.90 = Rs. 900 (for 950 g given). Step 3: Marked price = 1000 × 1.20 = Rs. 1200 (20% above original CP). Step 4: Actual SP = Rs. 1200 (he charges for 1000 g at marked price). Step 5: Profit = 1200 - 900 = Rs. 300. Step 6: Profit % = 300/900 × 100 = 33.33%.

Question 20

A merchant uses false weights and gives 1200 g instead of 1 kg. If he wants to make a profit of 20%, at what percentage above cost price should he mark his goods?

Accepted Answer

Step 1: He gives 1200 g but charges for 1000 g. Cost to merchant for 1200 g = 1200C. Step 2: He wants 20% profit, so SP = 1200C × 1.20 = 1440C. Step 3: This SP is for 1000 g charged. Step 4: Markup % = (1440C - 1000C) / 1000C × 100 = 440/1000 × 100 = 44%.

Question 21

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. Step 2: If cost price per gram is C, then cost to shopkeeper = 900C. Step 3: Selling price = 1000C (charged at cost price per gram). Step 4: Profit = (1000C - 900C) / 900C × 100 = 100C / 900C × 100 = 100/9 % ≈ 11.11%.

Question 22

A vendor uses 1.25 kg weight instead of 1 kg and claims to sell at cost price. What is the profit percentage?

Accepted Answer

Step 1: The vendor gives 1.25 kg but charges for 1 kg. Step 2: If cost price per kg = C, then cost to vendor = 1.25C. Step 3: Selling price = 1C (charged at cost price per kg). Step 4: This is a loss situation, not profit. Profit % = (1 - 1.25) / 1.25 × 100 = -0.25/1.25 × 100 = -20%. Step 5: Loss = 20%.

Question 23

A dishonest shopkeeper claims to sell goods at cost price but uses a false weight. He gives only 800 g when he should give 1000 g. What is his profit percentage?

Accepted Answer

Step 1: The shopkeeper gives 800 g but charges for 1000 g. Step 2: Cost Price for 800 g = Cost Price for 1000 g (since he claims to sell at CP). Step 3: Selling Price = Cost Price of 1000 g. Step 4: Actual Cost Price = Cost Price of 800 g = (800/1000) × CP of 1000 g = 0.8 × SP. Step 5: Profit % = [(SP - CP) / CP] × 100 = [(SP - 0.8×SP) / (0.8×SP)] × 100 = [0.2×SP / 0.8×SP] × 100 = (0.2/0.8) × 100 = 25%.

Question 24

A shopkeeper uses 900 g weight instead of 1 kg and also gives a 10% discount on the marked price. If the marked price is 50% above cost price, what is his net profit or loss percentage?

Accepted Answer

Step 1: Let CP per gram = Re. 1. Cost for 900 g = Rs. 900. Step 2: Marked price per gram = 1.50 (50% above CP). MP for 1000 g = 1000 × 1.50 = Rs. 1500. Step 3: After 10% discount, SP = 1500 × 0.90 = Rs. 1350. Step 4: Profit = 1350 - 900 = Rs. 450. Step 5: Profit % = 450/900 × 100 = 50%.

Question 25

A fraudulent dealer uses weights such that he gives only 800 g when 1 kg is demanded. If he marks up his goods by 25% above cost price and then sells at marked price, what is his total profit percentage?

Accepted Answer

Step 1: Let cost price per gram = Re. 1. Cost to dealer for 800 g = Rs. 800. Step 2: Marked price per gram = 1.25 (25% markup). Selling price for 1000 g charged = 1000 × 1.25 = Rs. 1250. Step 3: Profit = 1250 - 800 = Rs. 450. Step 4: Profit % = 450/800 × 100 = 56.25%.

Question 26

A merchant uses 800 g weights instead of 1 kg while buying goods from wholesalers and sells at marked price using correct weights. If his cost price per kg is ₹100, what is his profit percentage?

Accepted Answer

Step 1: While buying, merchant pays for 800 g but receives 1000 g (using false weight). Effective cost per 1000 g = (800/1000) × 100 = ₹80. Step 2: Selling price per 1000 g = ₹100 (marked price, correct weight). Step 3: Profit% = [(100 - 80) / 80] × 100 = (20/80) × 100 = 25%.

Question 27

A merchant buys sugar at ₹20 per kg. While selling, he uses weights such that 1200 g is marked as 1 kg, and he sells at ₹25 per kg (marked). What is his profit percentage?

Accepted Answer

Step 1: The merchant actually gives 1200 g but charges for 1000 g. Step 2: Cost Price for 1200 g = (20 × 1200)/1000 = ₹24. Step 3: Selling Price for 1200 g = ₹25 (charged as 1 kg). Step 4: Profit = 25 - 24 = ₹1. Step 5: Profit % = (1/24) × 100 = 4.17% ≈ 4.2%.

Question 28

A dishonest grocer claims to sell at cost price but uses a faulty balance. When he should give 1 kg, his balance shows 1.25 kg. If the cost price is ₹40 per kg, what is his profit percentage?

Accepted Answer

Step 1: The grocer's balance is faulty; it shows 1.25 kg when actual weight is 1 kg. Step 2: When the customer thinks they are buying 1.25 kg (as shown on balance), they actually receive 1 kg. Step 3: Cost Price for 1 kg = ₹40. Step 4: Selling Price charged = ₹40 × 1.25 = ₹50 (customer pays for 1.25 kg at ₹40/kg). Step 5: Profit = 50 - 40 = ₹10. Step 6: Profit % = (10/40) × 100 = 25%.

Question 29

A dishonest shopkeeper claims to sell goods at cost price but uses false weights. He gives only 800 g when he should give 1000 g. What is his profit percentage?

Accepted Answer

Step 1: The shopkeeper receives payment for 1000 g but gives only 800 g. Step 2: Cost Price (CP) for 800 g = CP for 800 g. Selling Price (SP) for 800 g = CP for 1000 g. Step 3: Profit = SP - CP = CP(1000) - CP(800) = CP(200). Step 4: Profit % = (200/800) × 100 = 25%.

Question 30

A fraudulent dealer buys goods at ₹10 per kg and sells at ₹12 per kg, but uses a 900 g weight instead of 1 kg. What is his total profit percentage?

Accepted Answer

Step 1: For every 900 g sold, the dealer charges ₹12 (price of 1 kg). Step 2: Cost Price for 900 g = (10 × 900)/1000 = ₹9. Step 3: Selling Price for 900 g = ₹12. Step 4: Profit = 12 - 9 = ₹3. Step 5: Profit % = (3/9) × 100 = 33.33%.

Question 31

A shopkeeper buys goods at ₹50 per kg using false weights (950 g instead of 1 kg) and sells at ₹60 per kg using correct weights. What is his profit percentage?

Accepted Answer

Step 1: While buying, shopkeeper pays ₹50 for 950 g but receives 1000 g. Effective cost per 1000 g = (950/1000) × 50 = ₹47.50. Step 2: Selling price per 1000 g = ₹60. Step 3: Profit% = [(60 - 47.50) / 47.50] × 100 = (12.50 / 47.50) × 100 = 26.31% ≈ 26⅜%.

Question 32

A fraudulent merchant uses weights of 800 g for 1 kg while buying and weights of 1200 g for 1 kg while selling. If he claims to sell at cost price, what is his actual profit percentage?

Accepted Answer

Step 1: While buying: He pays for 1 kg but receives 1000 g (his weight shows 800 g = 1 kg, so actual = 1000/0.8 = 1250 g per his 1 kg). Actually, when he uses 800 g weight for 1 kg purchase, he gets 1000 g for the price of 800 g. Cost Price per g = 1/0.8 = 1.25 units. Step 2: While selling: He gives 1000 g but charges for 1200 g (his weight shows 1200 g = 1 kg, so he gives less). He gives 1000/1.2 = 833.33 g but charges for 1 kg. Selling Price per g = 1/0.833 = 1.2 units. Step 3: For 1000 g actual goods: CP = 1000 × (0.8/1) = 800 units. SP = 1000 × (1.2/1) = 1200 units. Step 4: Profit % = [(1200 - 800)/800] × 100 = 50%.

Question 33

A dealer buys sugar at ₹40 per kg. He uses false weights and sells at ₹50 per kg. If his profit is 37.5%, how much less weight (in grams) does he give for 1 kg?

Accepted Answer

Step 1: Let actual weight given = x grams. CP for x grams = 40x/1000. SP for x grams = 50 × 1 = ₹50 (charged as 1 kg). Step 2: Profit% = (SP - CP)/CP × 100. 37.5 = (50 - 40x/1000)/(40x/1000) × 100. Step 3: 0.375 = (50 - 0.04x)/(0.04x). 0.375 × 0.04x = 50 - 0.04x. 0.015x = 50 - 0.04x. 0.055x = 50. x = 909.09 g. Step 4: Weight short = 1000 - 909.09 ≈ 91 g (or exactly 1000/11 ≈ 90.91 g).

Question 34

A merchant uses 1200 g weights instead of 1 kg while buying and 800 g weights instead of 1 kg while selling. He buys at ₹50 per kg and sells at ₹75 per kg. What is his net profit percentage?

Accepted Answer

Step 1: While buying 1 kg (charged), he actually receives 1200 g. CP per gram = 50/1000 = ₹0.05. CP for 1200 g = 1200 × 0.05 = ₹60. Step 2: While selling 1 kg (charged), he gives only 800 g. SP per gram = 75/1000 = ₹0.075. SP for 800 g = 800 × 0.075 = ₹60. Step 3: But he has 1200 g from buying. From 1200 g, he can make 1200/800 = 1.5 batches of 800 g each. Total SP = 1.5 × 60 = ₹90. Step 4: Profit% = (90 - 60)/60 × 100 = 30/60 × 100 = 50%.

Question 35

A shopkeeper uses weights of 950 g for 1 kg and also gives a 5% discount on the marked price. If his cost price is ₹100 per kg, what is his net profit or loss percentage?

Accepted Answer

Step 1: CP per gram = ₹0.1, so CP for 950 g = ₹95. Step 2: Let MP per kg = ₹100. SP per kg = 100 × 0.95 = ₹95. Step 3: SP for 950 g = 95 × 0.95 = ₹90.25. Step 4: Profit/Loss% = (90.25 - 95)/95 × 100 = -4.75/95 × 100 = -5%.

Question 36

A fraudulent dealer buys goods at ₹10 per kg and sells using 750 g weights instead of 1 kg, claiming to sell at ₹12 per kg. What is his actual profit percentage?

Accepted Answer

Step 1: CP per kg = ₹10, so CP per gram = ₹0.01. CP for 750 g = ₹7.50. Step 2: He claims to sell at ₹12 per kg, so for 750 g he charges ₹12 × 0.75 = ₹9. Step 3: Profit% = (9 - 7.50)/7.50 × 100 = 1.50/7.50 × 100 = 20%.

Question 37

A dealer uses 950 g weights instead of 1 kg while selling. To earn a profit of 20% on cost price, at what percentage above cost price should he mark his goods (assuming he sells at marked price)?

Accepted Answer

Step 1: Let CP per gram = ₹1. For 1000 g actual goods, CP = ₹1000. Step 2: He wants 20% profit, so SP should be = 1000 × 1.2 = ₹1200. Step 3: But he gives only 950 g and charges as if it were 1000 g. So for 950 g, he charges ₹1000 (marked price). Step 4: To get SP of ₹1200 for 950 g, he must mark price at ₹1200 for 950 g. Step 5: Markup % = [(1200 - 1000)/1000] × 100 = 20%. Wait, recalculate: He gives 950 g but charges for 1000 g at marked price. If MP = x per gram, then for 950 g he collects 950x. For 20% profit on 950 g: 950x = 950 × 1 × 1.2 = 1140. So x = 1.2 per gram. Markup % = [(1.2 - 1)/1] × 100 = 20%. But he's already gaining from false weight. Let me reconsider: CP for 950 g = 950. To get 20% profit on this 950 g: SP = 950 × 1.2 = 1140. He charges for 1000 g at MP, so 1000 × MP = 1140, thus MP = 1.14 per gram. Markup % = [(1.14 - 1)/1] × 100 = 14%.

Question 38

A merchant uses 800 g weights instead of 1 kg and sells at 25% markup on cost price. What is his total profit percentage?

Accepted Answer

Step 1: For 800 g actual goods, he charges as if selling 1000 g. Step 2: Let CP per gram = ₹1. CP for 800 g = ₹800. SP for 800 g = 1000 × 1.25 = ₹1250 (1 kg at 25% markup). Step 3: Profit% = (1250 - 800)/800 × 100 = 450/800 × 100 = 56.25%.

ITBP Constable False Weight / Fraudulent Dealer

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