Question 1

A 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: Profit = 1000 - 900 = 100 g on every 900 g given. Step 3: Profit % = (Error / True Value - Error) × 100 = (100 / 900) × 100 = 100/9 = 11.11%. Therefore, answer is 11 1/9%.

Question 2

A dishonest shopkeeper claims to sell goods at cost price, but uses false weights. He gives only 800 grams when he should give 1000 grams for every kilogram sold. 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 claimed).

Step 2: He gives 800 g but charges for 1000 g. This means:
- Cost incurred by shopkeeper = 800 g at cost price
- Revenue received = Price of 1000 g at cost price (since he claims to sell at CP)

Step 3: Let cost price per gram = C
- Actual Cost = 800C
- Selling Price = 1000C (he charges the price for 1000 g)

Step 4: Profit = SP - CP = 1000C - 800C = 200C

Step 5: Profit % = (Profit / CP) × 100
Profit % = (200C / 800C) × 100
Profit % = (200/800) × 100
Profit % = (1/4) × 100
Profit % = 25%

Therefore, the profit percentage is 25%.

Question 3

A vendor uses 950 g weights instead of 1 kg while selling sugar. If he sells at a price 5% lower than the market rate, what is his overall profit or loss percentage?

Accepted Answer

Step 1: Using 950 g weight instead of 1000 g means he gives 950 g but charges for 1000 g. Step 2: If market rate per gram = R, then he charges at 0.95R per gram (5% lower). Step 3: For 1000 g charged, he actually gives 950 g. Step 4: CP of 950 g = 950R, SP = 1000 × 0.95R = 950R. Step 5: Profit/Loss = 950R - 950R = 0. Step 6: There is no profit or loss; he breaks even.

Question 4

A dishonest shopkeeper claims to sell goods at cost price but uses a false weight of 800 g instead of 1 kg. What is his profit percentage?

Accepted Answer

Step 1: The shopkeeper gives only 800 g but charges for 1000 g (1 kg). Step 2: If cost price per gram is C, then cost to shopkeeper = 800C. Step 3: Selling price (what customer pays) = 1000C. Step 4: Profit = SP - CP = 1000C - 800C = 200C. Step 5: Profit % = (200C / 800C) × 100 = 25%. Therefore, the answer is 25%.

Question 5

A dishonest grocer uses 750 g weights instead of 1 kg while selling rice. He also marks up the price by 20% above cost price. What is his overall profit percentage?

Accepted Answer

Step 1: Using 750 g weight instead of 1000 g means he gives 750 g but charges for 1000 g. Step 2: If CP per gram = C, then CP of 750 g = 750C, but he charges for 1000 g at marked price. Step 3: Marked price per gram = 1.2C (20% markup on CP). Step 4: SP for 1000 g charged = 1000 × 1.2C = 1200C. Step 5: Actual CP of 750 g given = 750C. Step 6: Profit = 1200C - 750C = 450C. Step 7: Profit % = (450C / 750C) × 100 = 60%.

Question 6

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: When the shopkeeper uses 800 g instead of 1000 g, he gives 800 g but charges for 1000 g. Step 2: If cost price per gram is C, then Cost Price for 800 g = 800C, but Selling Price = 1000C. Step 3: Profit = 1000C - 800C = 200C. Step 4: Profit % = (200C / 800C) × 100 = 25%.

Question 7

A shopkeeper uses 1.25 kg weight instead of 1 kg and sells at cost price. What is his profit percentage?

Accepted Answer

Step 1: The shopkeeper gives 1.25 kg but charges for only 1 kg. Step 2: If cost price per kg is C, then CP for 1.25 kg = 1.25C. Step 3: SP (what customer pays for 1 kg) = 1C. Step 4: This is a loss situation: Loss = 1.25C - 1C = 0.25C. Step 5: Loss % = (0.25C / 1.25C) × 100 = 20%. Therefore, the answer is 20% loss (or -20% profit).

Question 8

A fraudulent dealer uses weights of 900 g for 1 kg while buying goods from the wholesaler. When selling to customers, he uses 1 kg weights correctly. If he buys and sells at the same rate per gram, what is his profit percentage?

Accepted Answer

Step 1: When buying, he uses 900 g weight but pays for 1000 g (gets 1000 g goods for price of 900 g). Step 2: When selling, he uses correct 1 kg weight and sells at same rate per gram. Step 3: For every 1000 g he receives, he pays for 900 g. Step 4: He sells 1000 g at the rate of 1000 g. Step 5: If rate per gram = R, then CP = 900R, SP = 1000R. Step 6: Profit % = [(1000R - 900R) / 900R] × 100 = (100/900) × 100 = 11.11%.

Question 9

A merchant uses 1100 g weights instead of 1 kg while buying from the wholesaler and uses 900 g weights instead of 1 kg while selling to customers. Both transactions occur at the same rate per gram. What is his profit percentage?

Accepted Answer

Step 1: While buying, he uses 1100 g weight, so he gets 1100 g but pays for only 1000 g. CP for 1100 g = 1000 units. Step 2: While selling, he uses 900 g weight, so he gives 900 g but charges for 1000 g. SP for 900 g = 1000 units. Step 3: Now we need a common quantity. LCM of 1100 and 900 = 9900. Step 4: In buying: For 9900 g, he pays = (9900/1100) × 1000 = 9 × 1000 = 9000 units. Step 5: In selling: For 9900 g, he receives = (9900/900) × 1000 = 11 × 1000 = 11000 units. Step 6: Profit = 11000 - 9000 = 2000 units. Step 7: Profit % = (2000/9000) × 100 = 22.22%.

Question 10

A merchant uses false weights while buying and selling. He buys goods using 1100 g weights (instead of 1 kg) and sells using 900 g weights (instead of 1 kg), both at the same price per kg. What is his profit percentage?

Accepted Answer

Step 1: While buying 1 kg (charged), he actually receives 1100 g. While selling 1 kg (charged), he gives only 900 g. Step 2: For every 1 kg charged to customer: CP = (1100/900) × 1 = 1.222 units. SP = 1 unit. Wait, recalculate: If he buys at price P per kg and sells at price P per kg. Step 3: He buys 1100 g for price of 1 kg. He sells 900 g for price of 1 kg. Step 4: To sell 1100 g, he needs (1100/900) kg worth of selling = (1100/900) × P. CP of 1100 g = 1 × P. Profit = [(1100P/900 - P)/P] × 100 = (1100/900 - 1) × 100 = (200/900) × 100 = 22.22%.

Question 11

A vendor buys apples at ₹100 per dozen but uses 10 apples as a dozen while selling at ₹100 per dozen. What is his profit percentage?

Accepted Answer

Step 1: The vendor buys 12 apples for ₹100 (actual dozen). Step 2: The vendor sells 10 apples for ₹100 (false dozen). Step 3: CP per apple = 100/12 = ₹8.33. SP per apple = 100/10 = ₹10. Step 4: Profit per apple = 10 - 8.33 = ₹1.67. Step 5: Profit% = (1.67/8.33) × 100 = 20%.

Question 12

A dealer sells sugar at ₹20 per kg using false weights. A customer who buys 5 kg (as per the dealer's weights) actually receives only 4 kg. If the dealer's cost price is ₹15 per kg, what is his profit percentage?

Accepted Answer

Step 1: Customer pays for 5 kg at ₹20/kg = ₹100 (SP). Step 2: Customer actually receives 4 kg, so CP = 4 × ₹15 = ₹60. Step 3: Profit = 100 - 60 = ₹40. Step 4: Profit % = (40/60) × 100 = 66.67% ≈ 66⅔%.

Question 13

A dishonest grocer buys rice at ₹24 per kg and sells at ₹30 per kg. He also uses a 750 g weight instead of 1 kg. What is his total profit percentage?

Accepted Answer

Step 1: For 750 g (actual), CP = 750 × (24/1000) = ₹18. Step 2: He charges for 1000 g, so SP = 1000 × (30/1000) = ₹30. Step 3: Profit = 30 - 18 = ₹12. Step 4: Profit % = (12/18) × 100 = 66.67% ≈ 66⅔%.

Question 14

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: For 800 g (actual weight), CP = 800 × (10/1000) = ₹8. Step 2: He charges for 1000 g, so SP = 1000 × (12/1000) = ₹12. Step 3: Profit = 12 - 8 = ₹4. Step 4: Profit % = (4/8) × 100 = 50%.

Question 15

A fraudulent dealer sells goods at 10% profit but uses weights such that 1 kg on his weighing scale is actually 900 g. What is his actual profit percentage?

Accepted Answer

Step 1: The dealer marks 10% profit on the selling price. For every 1000 g (marked), he charges 1.10 × CP. Step 2: But he actually gives only 900 g. Step 3: His actual cost for 900 g = 0.9 × CP. Step 4: His actual selling price = 1.10 × CP. Step 5: Actual profit = 1.10 × CP - 0.9 × CP = 0.20 × CP. Step 6: Actual profit % = (0.20 × CP)/(0.9 × CP) × 100 = (0.20/0.9) × 100 = 22.22%. Therefore, the answer is 22.22%.

Question 16

A merchant uses false weights while buying and selling. While buying, he uses 1200 g weights instead of 1000 g, and while selling, he uses 800 g weights instead of 1000 g. If he claims to sell at cost price, what is his actual profit percentage?

Accepted Answer

Step 1: While buying 1000 g (marked), he actually receives 1200 g. Cost = 1000 units. Step 2: While selling 1000 g (marked), he actually gives 800 g. Selling price = 1000 units. Step 3: For every 1000 units spent, he gets 1200 g of goods. Step 4: From 1200 g, he sells in batches of 800 g for 1000 units each. Step 5: From 1200 g, he can sell (1200/800) = 1.5 batches = 1500 units. Step 6: Profit = 1500 - 1000 = 500 units. Step 7: Profit % = (500/1000) × 100 = 50%. Therefore, the answer is 50%.

Question 17

A dishonest grocer gives only 950 g when a customer asks for 1 kg and charges the full price of 1 kg. Additionally, he adulterates the goods such that only 80% of the weight is pure. What is his total profit percentage?

Accepted Answer

Step 1: Customer pays for 1000 g at price P. Step 2: Grocer gives 950 g but only 80% is pure, so pure weight = 950 × 0.80 = 760 g. Step 3: Grocer's cost for 760 g of pure goods = 760 units. Step 4: Grocer's selling price = 1000 units. Step 5: Profit = 1000 - 760 = 240 units. Step 6: Profit % = (240/760) × 100 = 31.58% ≈ 31.6%. Therefore, the answer is 31.58%.

Question 18

A shopkeeper uses a faulty balance that reads 20% more than the actual weight when goods are placed on the left pan. He buys goods at ₹100 per kg (based on the faulty reading) and sells them at ₹120 per kg (also based on the faulty reading). What is his actual profit or loss percentage?

Accepted Answer

Step 1: When the balance shows 1 kg, actual weight is 1/1.2 = 0.833 kg. Step 2: Shopkeeper pays ₹100 per kg (faulty reading), so for goods showing 1 kg, he pays ₹100. Step 3: Actual weight received = 0.833 kg. Actual cost per kg = 100/0.833 = 120 per kg. Step 4: Shopkeeper sells at ₹120 per kg (faulty reading), so for goods showing 1 kg, he receives ₹120. Step 5: Actual weight sold = 0.833 kg. Actual revenue per kg = 120/0.833 = 144 per kg. Step 6: Profit per kg = 144 - 120 = 24 per kg. Step 7: Profit % = (24/120) × 100 = 20%. Therefore, the answer is 20% profit.

Question 19

A fraudulent merchant uses weights such that when he buys goods, he uses 1200 g weights instead of 1 kg, and when he sells, he uses 800 g weights instead of 1 kg. If he marks up the cost price by 25%, what is his overall profit percentage?

Accepted Answer

Step 1: When buying: He pays for 1000 g but receives 1200 g. Cost per gram = CP/1200. Step 2: When selling: He gives 800 g but charges for 1000 g at 25% markup. Selling price per gram = (1.25 × CP)/800. Step 3: For 1 kg (1000 g) purchased at actual cost = CP. Step 4: He receives 1200 g, sells it in batches of 800 g at marked-up price. Revenue from 1200 g = (1200/800) × 1.25 × CP = 1.5 × 1.25 × CP = 1.875 × CP. Step 5: Profit% = (1.875CP - CP)/CP × 100 = 0.875/1 × 100 = 87.5%.

Question 20

A dealer uses false weights while buying and selling. When buying, he uses 950 g for 1 kg, and when selling, he uses 1050 g for 1 kg. He buys at ₹40 per kg and sells at ₹50 per kg (marked price). What is his profit percentage?

Accepted Answer

Step 1: When buying 1 kg (marked), he actually receives 1000/950 kg = 1.0526 kg. Cost for this = 1.0526 × 40 = ₹42.11 (approximately). Step 2: When selling 1 kg (marked), he actually gives 1000/1050 kg = 0.9524 kg. Revenue = 1 × 50 = ₹50. Step 3: Profit per kg marked = 50 - 42.11 = ₹7.89. Step 4: Profit% = 7.89/42.11 × 100 ≈ 18.75%. Alternatively: Profit% = [(1000/950) × (1050/1000) × (50/40) - 1] × 100 = [(1000 × 1050 × 50)/(950 × 1000 × 40) - 1] × 100 = [(1050 × 50)/(950 × 40) - 1] × 100 = [52500/38000 - 1] × 100 = [1.3816 - 1] × 100 = 38.16%.

Question 21

A dishonest shopkeeper claims to sell goods at cost price but uses a faulty weight. 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 delivers only 800 g. Step 2: His cost price for 800 g = 800 units. Step 3: His selling price (what customer pays) = 1000 units. Step 4: Profit = 1000 - 800 = 200 units. Step 5: Profit % = (200/800) × 100 = 25%. Therefore, the answer is 25%.

SSC CHSL False Weight / Fraudulent Dealer

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False Weight / Fraudulent Dealer — Practice Questions

60-Second Revision — False Weight / Fraudulent Dealer