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 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?
Practice 2easy
A merchant buys goods at ₹500 per kg but uses a faulty weight that shows 1100 g when the actual weight is 1000 g. At what price per kg should he mark the goods to make a 10% profit?
Practice 3easy
A dishonest shopkeeper gives only 950 g when a customer asks for 1 kg and charges the full price of 1 kg. If the shopkeeper's cost price is ₹400 per kg, what is his profit percentage?
Practice 4easy
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 5easy
A shopkeeper uses 800 g weights instead of 1 kg while buying goods, and uses 1000 g weights instead of 1 kg while selling. What is his overall profit percentage?
Practice 6medium
A shopkeeper uses 950 g weights instead of 1 kg while selling. To make a profit of 20% on cost price, at what percentage above cost price should he mark his goods?
Practice 7medium
A merchant uses false weights and gains 25% while buying and 25% while selling. What is his total profit percentage?
Practice 8hard
A fraudulent dealer sells goods at 20% profit but uses weights such that 1200 g is marked as 1 kg on his balance. What is his actual profit percentage?
Practice 9hard
A dishonest trader uses weights such that 800 g is marked as 1 kg. He also offers a 10% discount on the marked price. What is his net profit or loss percentage?