Study Material — 2 PYQs (2018–2018) · Concept Notes · Shortcuts
SSC CHSL False Weight / Fraudulent Dealer is a frequently tested subtopic — 2 previous year questions from 2018–2018 papers are included below with concept notes, key rules and shortcut tricks.
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?
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 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?
Practice 2easy
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?
Practice 3easy
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?
Practice 4easy
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?
Practice 5easy
A shopkeeper uses 1.25 kg weight instead of 1 kg and sells at cost price. What is his profit percentage?
Practice 6easy
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?
Practice 7easy
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?
Practice 8medium
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?
Practice 9medium
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?
Practice 10medium
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?
Practice 11medium
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?
Practice 12medium
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?
Practice 13hard
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?
Practice 14hard
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?
Practice 15hard
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?
Practice 16hard
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?
Practice 17hard
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?
Practice 18hard
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?
Practice 19hard
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?