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 merchant uses false weights and gives 750 g instead of 1 kg. He sells at cost price. What is his profit percentage?
Practice 2easy
A dishonest dealer uses weights such that he gives 1100 g instead of 1 kg and also charges 10% extra. What is his profit percentage?
Practice 3easy
A dishonest grocer uses weights such that 1200 g is marked as 1 kg on his balance. If he sells at cost price, what is his profit percentage?
Practice 4easy
A vendor uses false weights and gives 1.2 kg when he should give 1 kg. He sells at cost price. What is his loss percentage?
Practice 5easy
A fraudulent merchant sells sugar at ₹20 per kg but uses a faulty weight of 800 grams for 1 kilogram. What is the actual cost price per kg if he makes a 25% profit?
Practice 6easy
A dishonest grocer uses 800 g weights instead of 1 kg while selling and claims to sell at cost price. What is his actual profit percentage?
Practice 7easy
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 8easy
A fraudulent dealer uses weights such that he gives 900 g for every 1 kg purchased. If he marks his goods at 20% above cost price, what is his overall profit percentage?
Practice 9medium
A shopkeeper buys goods at ₹100 per kg and sells using 800 g weights instead of 1 kg, claiming to sell at ₹125 per kg. What is his actual profit percentage?
Practice 10medium
A vendor uses a faulty balance where 1 kg mark actually represents 900 grams. He claims to sell at cost price. What is his profit percentage?
Practice 11medium
A dishonest merchant uses weights such that 1 kg of his weights actually weighs 1.25 kg. He buys goods at ₹60 per kg and sells at ₹75 per kg using his faulty weights. What is his profit percentage?
Practice 12medium
A grocer uses false weights. When he claims to give 1 kg, he actually gives only 800 grams. He also marks up the price by 25% above cost price. What is his actual profit percentage?
Practice 13medium
A dishonest shopkeeper buys goods at ₹100 per kg and sells at ₹120 per kg. Additionally, he uses a false weight of 800 g instead of 1 kg. What is his total profit percentage?
Practice 14medium
A vendor uses 1.2 kg weights instead of 1 kg while selling. If he sells at ₹50 per kg (marked weight), what is his loss percentage?
Practice 15hard
A dishonest dealer sells goods at 25% profit but uses false weights such that he gives only 750 g instead of 1 kg. If his cost price is ₹200 per kg, what is his actual profit percentage?
Practice 16hard
A shopkeeper uses false weights and claims to sell at cost price. When he buys goods, he uses weights that are 10% heavier than standard, and when he sells, he uses weights that are 10% lighter than standard. What is his profit percentage?
Practice 17hard
A fraudulent dealer 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 vendor buys apples at ₹80 per kg using false weights of 1200 g (pays for 1 kg, gets 1200 g). He sells at ₹100 per kg using false weights of 800 g (gives 800 g, charges for 1 kg). What is his profit percentage?
Practice 19hard
A merchant uses false weights while buying and selling. He buys goods at ₹100 per kg using 1100 g weights (i.e., he pays for 1 kg but receives 1100 g). He sells at ₹120 per kg using 900 g weights (i.e., he gives 900 g but charges for 1 kg). What is his overall profit percentage?
Practice 20hard
A dishonest grocer uses weights such that 1 kg weight actually weighs 960 g. He buys goods at ₹50 per kg and sells at ₹60 per kg (both transactions using his faulty weights). What is his profit percentage?
2 more practice questions in the Study Panel
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