Core ConceptRead 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.
Formula BlockMemorise — 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
Exam PatternsWhat 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.
ShortcutsUse 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.
Worked ExampleSolve 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.
A dealer uses 1200 g weights instead of 1 kg while buying. If he buys at ₹50 per kg and sells at ₹60 per kg (both at nominal rates), what is his profit percentage?
Practice 2easy
A merchant uses 1050 g weights instead of 1000 g while selling goods at cost price. What is his loss percentage?
Practice 3easy
A merchant uses 900 g weights instead of 1 kg while buying goods from wholesalers. If he buys at ₹100 per kg, what is his effective cost price per gram?
Practice 4medium
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 5medium
A dishonest merchant uses weights that are 20% less than the standard. If he sells at the marked price (which assumes standard weights), what is his profit percentage?
Practice 6medium
A shopkeeper buys goods at ₹500 per kg using false weights of 1.2 kg instead of 1 kg. He sells at ₹600 per kg using false weights of 0.9 kg instead of 1 kg. What is his profit percentage?
Practice 7medium
A vendor uses 1.25 kg weights instead of 1 kg to measure goods he buys, and uses 0.8 kg weights instead of 1 kg to measure goods he sells. If he marks up the selling price by 20% over cost price, what is his overall profit percentage?
Practice 8hard
A fraudulent dealer buys goods at ₹100 per kg but uses false weights. He sells at ₹120 per kg (marked weight) and makes a profit of 44%. What is the false weight he uses for 1 kg?
Practice 9hard
A vendor uses false weights and sells sugar at ₹60 per kg (marked). His false weight is such that he gives only 750 g for every 1 kg marked. If his cost price is ₹45 per kg, what is his profit percentage?
Practice 10hard
A merchant buys goods at ₹80 per kg. He uses false weights of 850 g per kg and also gives a discount of 5% on the marked price. If he still makes a profit of 25%, what is the marked price per kg?