Question 1

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: The shopkeeper gives only 800 g but charges for 1000 g. Step 2: If cost price per gram is C, then cost to shopkeeper = 800C, but selling price = 1000C. Step 3: Profit = 1000C - 800C = 200C. Step 4: Profit % = (200C / 800C) × 100 = 25%.

Question 2

A dishonest dealer uses 750 g weights instead of 1000 g while buying and uses 1000 g weights instead of 1250 g while selling. He claims to sell at cost price. What is his profit percentage?

Accepted Answer

Step 1: While buying: He uses 750 g weight, so he pays for 750 g but receives 1000 g. Cost = 750 units for 1000 g goods. Step 2: While selling: He uses 1000 g weight instead of 1250 g, so he gives 1000 g but charges for 1250 g. Revenue = 1250 units for 1000 g goods. Step 3: Cost per gram = 750/1000 = 0.75 units. Step 4: Selling price per gram = 1250/1000 = 1.25 units. Step 5: Profit per gram = 1.25 - 0.75 = 0.5 units. Step 6: Profit % = (0.5 / 0.75) × 100 = 66.67%.

Question 3

A dealer uses 950 g weights instead of 1000 g while buying goods. He sells at cost price using correct weights. What is his profit percentage?

Accepted Answer

Step 1: While buying, he uses 950 g weight, so he pays for 950 g but receives 1000 g. Step 2: Cost to him = 950 units for 1000 g goods. Step 3: While selling, he uses correct 1000 g weight and sells at cost price. Step 4: Selling price = 1000 units for 1000 g. Step 5: Cost per gram = 950/1000 = 0.95 units. Step 6: Selling price per gram = 1000/1000 = 1 unit. Step 7: Profit % = [(1 - 0.95) / 0.95] × 100 = (0.05/0.95) × 100 = 5.26%.

Question 4

A fraudulent dealer uses 900 g weights instead of 1 kg while buying goods at cost price. When selling, he uses correct weights but claims to sell at cost price. What is his overall profit percentage?

Accepted Answer

Step 1: While buying: He pays for 900 g but receives 1000 g (uses 900 g weight). Cost to him = 900 units for 1000 g goods. Step 2: While selling: He gives 1000 g at cost price of 1000 units (correct weight). Step 3: His cost per gram = 900/1000 = 0.9 units. Step 4: His selling price per gram = 1000/1000 = 1 unit. Step 5: Profit % = [(1 - 0.9) / 0.9] × 100 = (0.1/0.9) × 100 = 11.11% ≈ 11.11%.

Question 5

A shopkeeper uses 900 g weights instead of 1 kg while selling. To earn a profit of 25%, at what price per kg should he sell if the cost price is ₹80 per kg?

Accepted Answer

Step 1: He uses 900 g false weight, so he gives 900 g but charges for 1000 g. Step 2: For 900 g (cost = 900 × 80/1000 = ₹72), he wants 25% profit. Step 3: Selling price for 900 g = 72 × 1.25 = ₹90. Step 4: This ₹90 is charged for 1000 g (due to false weight). Step 5: Selling price per kg = ₹90.

Question 6

A vendor uses 750 g instead of 1 kg while selling and 1.2 kg instead of 1 kg while buying. If his cost price is ₹40 per kg and he sells at ₹60 per kg, what is his profit percentage?

Accepted Answer

Step 1: While buying: He uses 1.2 kg false weight, so he gets 1.2 kg but pays for 1 kg at ₹40. Effective cost = 40/1.2 = ₹33.33 per kg. Step 2: While selling: He uses 750 g false weight, so he gives 750 g but charges for 1000 g at ₹60. Effective selling price = 60 × (1000/750) = 60 × 4/3 = ₹80 per kg. Step 3: Profit per kg = 80 - 33.33 = 46.67. Step 4: Profit % = (46.67 / 33.33) × 100 = 140%.

Question 7

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 is C per gram, he spends 900C but receives 1000C. Step 3: Profit = (1000C - 900C) / 900C × 100 = 100C / 900C × 100 = 100/9 % ≈ 11.11%. Step 4: Exact answer = 11⅑% or 100/9 %.

Question 8

A fraudulent dealer claims to sell at cost price but uses 950 g weights instead of 1 kg. A customer buys goods worth ₹1000 at marked price. How much less does the customer actually receive in terms of quantity?

Accepted Answer

Step 1: Customer pays ₹1000 at marked price, expecting 1000 g per ₹1 (assuming ₹1 per gram for simplicity, or any unit). Step 2: With false weight of 950 g, the customer receives only 950 g for every 1000 g worth of payment. Step 3: For ₹1000 payment, customer should get 1000 units, but gets only 950 units. Step 4: Shortfall = 1000 - 950 = 50 units. Step 5: Percentage shortfall = (50/1000) × 100 = 5%.

Question 9

A fraudulent dealer buys goods at ₹10 per kg and sells at ₹15 per kg. However, he uses a faulty balance that shows 1 kg when the actual weight is 1.25 kg. What is his overall profit percentage?

Accepted Answer

Step 1: The dealer's cost price = ₹10 per kg (actual). Step 2: His selling price = ₹15 per kg (as shown on faulty balance). Step 3: When the balance shows 1 kg sold, he actually gives 1.25 kg. Step 4: For 1 kg shown on balance: He receives ₹15 but gives away 1.25 kg costing him ₹10 × 1.25 = ₹12.50. Step 5: Profit per kg shown = 15 - 12.50 = ₹2.50. Step 6: Profit % = (2.50/12.50) × 100 = 20%.

Question 10

A shopkeeper uses a weighing machine that reads 1.1 kg when the actual weight is 1 kg. He buys goods at ₹80 per kg and sells at ₹100 per kg (both prices based on actual weight). What is his profit percentage?

Accepted Answer

Step 1: The machine reads 1.1 kg for actual 1 kg (vendor gives less than claimed). Step 2: When buying: He pays for 1.1 kg (as per machine) but receives 1 kg (actual). Cost = ₹80 × 1.1 = ₹88 for 1 kg actual. Step 3: When selling: He gives 1 kg (actual) but the machine shows 1.1 kg, so he charges for 1.1 kg. Revenue = ₹100 × 1.1 = ₹110 for 1 kg actual. Step 4: Profit = 110 - 88 = ₹22. Step 5: Profit % = (22/88) × 100 = 25%.

Question 11

A vendor uses a faulty balance that reads 1 kg when the actual weight is 800 g. He buys goods at ₹60 per kg and sells at ₹75 per kg. What is his profit percentage?

Accepted Answer

Step 1: The balance reads 1 kg for actual 800 g (vendor gives less than claimed). Step 2: When buying: He pays for 1 kg (as per balance) but receives only 800 g (actual). Cost = ₹60 for 800 g actual. Step 3: When selling: He gives 800 g (actual) but the balance shows 1 kg, so he charges for 1 kg. Revenue = ₹75 for 800 g actual. Step 4: Profit = 75 - 60 = ₹15. Step 5: Profit % = (15/60) × 100 = 25%.

Question 12

A dishonest grocer claims to sell sugar at ₹50 per kg but uses weights such that 1200 g is marked as 1 kg. Additionally, he mixes 20% sand with the sugar. If his cost price is ₹40 per kg of pure sugar, what is his profit percentage?

Accepted Answer

Step 1: Cost price of pure sugar = ₹40 per kg. Step 2: He mixes 20% sand, so in 1 kg of mixture, 800 g is sugar (cost = ₹40 × 0.8 = ₹32) and 200 g is sand (cost ≈ ₹0). Total cost for 1 kg mixture = ₹32. Step 3: His balance shows 1 kg when actual is 1200 g. Step 4: He sells 1200 g mixture (shown as 1 kg) at ₹50. Step 5: Cost of 1200 g mixture = ₹32 × 1.2 = ₹38.40. Step 6: Profit = 50 - 38.40 = ₹11.60. Step 7: Profit % = (11.60/38.40) × 100 ≈ 30.21% ≈ 30%.

Question 13

A dishonest shopkeeper claims to sell goods at cost price but uses a faulty weighing 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 (CP = SP per gram basis). Step 2: For every 1000 g of goods he should sell, he only gives 800 g but charges for 1000 g. Step 3: If cost price of 1000 g = ₹1000, then he pays ₹800 (for 800 g) but receives ₹1000. Step 4: Profit = 1000 - 800 = ₹200. Step 5: Profit % = (200/800) × 100 = 25%.

Question 14

A merchant uses a weighing machine that reads 900 g when the actual weight is 1 kg. He buys goods at ₹100 per kg and sells at ₹120 per kg (both at actual weight). What is his profit percentage?

Accepted Answer

Step 1: The machine reads 900 g for actual 1 kg. Step 2: When buying: He pays for 900 g (as per machine) but receives 1 kg (actual). Cost = ₹100 × 0.9 = ₹90 for 1 kg actual. Step 3: When selling: He gives 1 kg (actual) but the machine shows 900 g, so he charges for 900 g. Revenue = ₹120 × 0.9 = ₹108 for 1 kg actual. Step 4: Profit = 108 - 90 = ₹18. Step 5: Profit % = (18/90) × 100 = 20%.

SSC MTS False Weight / Fraudulent Dealer

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