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 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 2easy
A dishonest vendor uses weights of 950 g instead of 1 kg while selling sugar. He buys sugar at ₹80 per kg and sells at ₹80 per kg. What is his profit percentage?
Practice 3easy
A merchant uses 1200 g weights instead of 1 kg while selling. If he buys goods at ₹50 per kg and sells at ₹60 per kg (marked price), what is his profit percentage?
Practice 4easy
A fraudulent dealer uses 900 g weights instead of 1 kg while buying goods from wholesalers. If he buys at ₹100 per kg, what is his profit percentage when he sells at the marked price?
Practice 5easy
A shopkeeper uses 1250 g weights instead of 1 kg while selling. If his cost price is ₹40 per kg and he wants a profit of 25%, at what price per kg should he mark his goods?
Practice 6easy
A grocer uses 1100 g weights instead of 1 kg while buying from the wholesaler at ₹60 per kg. He then sells at ₹60 per kg using correct weights. What is his loss percentage?
Practice 7hard
A dishonest dealer mixes two types of goods: Type A (cost ₹100/kg) and Type B (cost ₹80/kg) in the ratio 3:2. He uses false weights such that 1000 g is marked as 1200 g on his balance. He sells the mixture at ₹120/kg (marked). What is his profit percentage?
Practice 8hard
A vendor uses false weights for both buying and selling. When buying, he uses 1100 g weights instead of 1000 g. When selling, he uses 900 g weights instead of 1000 g. If he buys at ₹50 per kg and sells at ₹60 per kg (both at marked rates), what is his profit percentage?
Practice 9hard
A fraudulent dealer sells goods at 10% profit but uses weights such that 900 g is marked as 1000 g on his balance. What is his actual profit percentage?
Practice 10hard
A dishonest shopkeeper claims to sell goods at cost price but uses a faulty balance. When he buys goods, he uses 1200 g weights instead of 1000 g, and when he sells, he uses 800 g weights instead of 1000 g. What is his overall profit percentage?