Study Material — 18 PYQs (2018–2024) · Concept Notes · Shortcuts
MP Police Constable False Weight / Fraudulent Dealer is a frequently tested subtopic — 18 previous year questions from 2018–2024 papers are included below with concept notes, key rules and shortcut tricks.
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?
Exam Q 32018Previous Year Pattern
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?
Exam Q 42024Previous Year Pattern
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?
Exam Q 52024Previous Year Pattern
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?
Exam Q 62024Previous Year Pattern
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?
Exam Q 72019Previous Year Pattern
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?
Exam Q 82024Previous Year Pattern
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?
Exam Q 92024Previous Year Pattern
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?
Exam Q 102024Previous Year Pattern
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?
Exam Q 112024Previous Year Pattern
A merchant uses 800 g weights instead of 1 kg and sells at 25% profit on cost price. What is the effective profit percentage?
Exam Q 122024Previous Year Pattern
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?
Exam Q 132024Previous Year Pattern
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?
Exam Q 142024Previous Year Pattern
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?
Exam Q 152024Previous Year Pattern
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?
Exam Q 162024Previous Year Pattern
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?
Exam Q 172024Previous Year Pattern
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?
Exam Q 182024Previous Year Pattern
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?
Concept Notes
False Weight / Fraudulent Dealer— Rules & Concept
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Core Concept
Read this first — the foundation of the topic
→Core Concept
A dealer uses false weights to gain extra profit. He might use a lighter weight while buying (getting more quantity for same price) or a heavier weight while selling (charging more for less quantity). Sometimes he does both
💡Key Rules
When a dealer uses weight 'w' grams instead of 1000 grams, his gain percentage = [(1000-w)/w] × 100. If he uses heavier weight while selling, gain = [(w-1000)/1000] × 100. For combined fraud (both buying and selling), multiply both gain factors.
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Formula Block
Memorise — at least one formula appears in every paper
• Gain% when using lighter weight for buying = [(True weight - False weight)/False weight] × 100
• Gain% when using heavier weight for selling = [(False weight - True weight)/True weight] × 100
• Overall gain% = [(CP with false weight)/(Actual CP)] × [(SP with false weight)/(Actual SP)] - 1
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Exam Patterns
What examiners ask — read before attempting PYQs
SSC asks three main types - (1) Find gain% when false weight is given, (2) Find false weight when gain% is given, (3) Combined buying-selling fraud problems. Questions often involve 900g, 800g weights instead of 1kg, or 1200g, 1100g for selling.
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Shortcuts
Use these to save 30–60 seconds per question
For buying with lighter weight - if dealer uses 800g instead of 1000g, he gains 200g extra on every 800g. So gain% = 200/800 = 25%. Quick formula: Extra weight/False weight × 100.
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Worked Example
Solve this step-by-step before moving on
1
Step 1
Calculate gain% in buying.
Using 900g instead of 1000g means getting 1000g quantity for price of 900g.
Gain% in buying = (1000-900)/900 × 100 = 100/900 × 100 = 11.11%
This means CP becomes 100/111.11 = 90% of actual.
2
Step 2
Calculate gain% in selling.
Using 1100g instead of 1000g means customer pays for 1100g but gets 1000g.
Gain% in selling = (1100-1000)/1000 × 100 = 10%
This means SP becomes 110% of actual.
3
Step 3
Find overall gain%.
Overall gain% = (0.90 × 1.10 - 1) × 100 = (0.99 - 1) × 100 = -1%
Wait, this is wrong approach.
Correct Method:
Effective CP ratio = 900:1000 = 9:10
Effective SP ratio = 1100:1000 = 11:10
Gain% = [(11/10)/(9/10) - 1] × 100 = [11/9 - 1] × 100 = 2/9 × 100 = 22.22%
Common Mistake: Students often confuse whether the dealer is buying or selling, and apply wrong formula. Always identify the transaction type first.
Key Points to Remember
False weight = dealer uses incorrect weights to cheat customers and gain extra profit
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?
Practice 2easy
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?
Practice 3easy
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?
Practice 4easy
A vendor uses 1.25 kg weight instead of 1 kg and claims to sell at cost price. What is the profit percentage?
Practice 5easy
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?
Practice 6easy
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?
Practice 7easy
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?
Practice 8medium
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?
Practice 9medium
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?
Practice 10medium
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?
Practice 11medium
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?
Practice 12medium
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?
Practice 13medium
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?
Practice 14hard
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)?
Practice 15hard
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?
Practice 16hard
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?
Practice 17hard
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?
Practice 18hard
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?
Practice 19hard
A merchant uses 800 g weights instead of 1 kg and sells at 25% markup on cost price. What is his total profit percentage?
Practice 20hard
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?