Dishonest Dealer: False Weights, Cheating and Adulteration
Dishonest Dealer: False Weights, Cheating and Adulteration
A dishonest dealer earns his profit by changing the QUANTITY, not the price: a short weight, a long measure while buying, or water in the milk. The trick is to compare what he pays for with what he charges for, using one formula that covers all three cases.
1. The One Formula
Profit % = (What he charges for − What he actually gives) / What he actually gives × 100, when he sells at cost price
| Case | Gain % | Example |
|---|---|---|
| False weight, sells at CP | (True − False)/False × 100 = Error/(True − Error) × 100 | 900 g for 1 kg: 100/900 = 11 1/9% |
| Weight short by e%, sells at CP | e/(100 − e) × 100 | 20% short weight gives 25% gain |
| False weight and a price mark-up of m% | [(100 + m)/100 × True/False − 1] × 100 | 960 g and 5% above CP gives 9.375% |
| Takes x% extra while buying, gives y% less while selling | [(100 + x)/(100 − y) − 1] × 100 | 10% each way gives (110/90 − 1) × 100 = 22 2/9% |
| "Cheats by x% while buying and y% while selling" with no quantity detail | [(1 + x/100)(1 + y/100) − 1] × 100, the reading used in most answer keys | 10% each way gives 21% |
| Mixes water w with milk m, sells at CP of milk | w/m × 100 | 1 L water per 4 L milk gives 25% |
| Profit p% on SP | On CP it is [p/(100 − p)] × 100 | 20% on SP = 25% on CP |
✗ 900 g for 1 kg gives 10% profit | ✓ The base is what he gives: 100 g extra charged on 900 g = 11 1/9%
Two readings exist for cheating questions. If the question says he GIVES x% less quantity (90 g for 100 g), divide by (100 − x). If it only says he "cheats by x%" on both sides, answer keys usually multiply 1.1 × 1.1 = 1.21, that is 21%. Read the wording first; the options normally contain only one of 21% and 22 2/9%.
✗ Water is 20% of the mixture, so profit 20% | ✓ If water is 20% of the mixture, milk is 80%; profit = 20/80 = 25% when sold at the CP of milk
2. How to Read Cheating Statements
| Statement | Translate as |
|---|---|
| Uses a weight of 960 g for 1 kg | Gives 960, charges for 1,000 |
| Weight is 20% short | Gives 80, charges for 100 |
| Takes 10% extra while buying | Takes 110 units, pays for 100 |
| Gives 10% less while selling | Gives 90 units, charges for 100 (factor 100/90) |
| Only "cheats by 10% while selling" | Answer keys usually treat it as charging 10% more (factor 1.1) |
| Sells at 4% loss on CP (nominally) | Charges 96 for each 100 of cost-price value |
हिंदी नोट: बेईमान दुकानदार कीमत नहीं, मात्रा बदलता है। लाभ प्रतिशत हमेशा उस मात्रा पर निकालिए जो वह वास्तव में देता है, जैसे 900 ग्राम देकर 1 किलो के पैसे लेने पर लाभ 100/900 = 11 1/9% होता है।
Exam Pointer: A false-weight question (weight short by a percentage while claiming to sell at cost price) came in the October 2025 Graduate CBT-2. Cheating on both sides, adulteration and profit-on-SP conversions had no verified NTPC shift in our check, so they are tagged syllabus-based; they use the same quantity-comparison idea, so learn them together.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: False weight, with or without a price mark-up
[PYQ: NTPC Graduate CBT-2 13-Oct-2025 Shift-2]
EXAM LEVEL
Q. A shopkeeper claims to sell at cost price but uses a weight of 900 g in place of 1 kg. Find his gain percent.
He gives 900 g and charges for 1,000 g. Gain = 100/900 × 100 = 11 1/9%.
Answer: 11 1/9%
EXAMATLAS LEVEL
Q. A dealer uses a 960 g weight for 1 kg and also sells his goods at 5% above cost price. Find his gain percent.
For 960 g he receives the price of 1,000 g plus 5%, that is 1,050 units of cost-value. Gain = 1,050/960 − 1 = 0.09375 = 9.375%. Adding 4% + 5% = 9% ignores the change of base.
Answer: 9.375%
Pattern 2: Cheating while buying and while selling
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A trader cheats his supplier and his customer by 10% each, taking 10% extra when buying and giving 10% less when selling, and claims to sell at cost price. Find his gain percent.
He gets 110 g for the price of 100 g and sells 90 g for the price of 100 g. Gain = (110/90 − 1) × 100 = 2/9 × 100 = 22 2/9%. The answer 20% (10 + 10) is the trap. If a question only says he "cheats by 10% while buying and selling" without saying that he gives less quantity, answer keys usually take 1.1 × 1.1 − 1 = 21%, so read the wording before choosing between 21% and 22 2/9%.
Answer: 22 2/9%
EXAMATLAS LEVEL
Q. A shopkeeper takes 20% extra quantity when buying, gives 20% less quantity when selling, and also charges 4% below the cost price. Find his actual gain percent.
Cost per gram he actually pays = 100/120. Revenue per gram he actually gives = 96/80 = 1.2 (he charges 96 for what should be 100 g but hands over only 80 g). Gain factor = 1.2 ÷ (100/120) = 1.2 × 1.2 = 1.44, a 44% gain despite the "loss" label.
Answer: 44%
Pattern 3: Adulteration: mixing water or impurity
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A milkman mixes 1 litre of water with every 4 litres of milk and sells the mixture at the cost price of milk. Find his gain percent.
He sells 5 litres for the price of 5 litres of milk but pays for only 4. Gain = 1/4 × 100 = 25%.
Answer: 25%
EXAMATLAS LEVEL
Q. A milkman buys milk at ₹48 per litre, adds water so that water is 20% of the mixture, and sells the mixture at ₹54 per litre. Find his gain percent.
One litre of mixture contains 0.8 L of milk costing 0.8 × 48 = ₹38.40. He sells it for ₹54. Gain = (54 − 38.40)/38.40 × 100 = 15.60/38.40 × 100 = 40.625%.
Answer: 40.625%
Pattern 4: Profit percent on selling price vs on cost price
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A shopkeeper's profit is 20% of his selling price. What is his profit as a percent of cost price?
Take SP = 100, profit = 20, so CP = 80. Profit on CP = 20/80 × 100 = 25%.
Answer: 25%
EXAMATLAS LEVEL
Q. A man sells an article at a profit of 20% of the selling price. Had he taken a profit of 20% on the cost price instead, he would have received ₹80 less. Find the cost price.
Profit 20% on SP means CP = 0.8 SP, so SP₁ = 1.25 CP. Profit 20% on CP gives SP₂ = 1.2 CP. The difference 0.05 CP = 80, so CP = ₹1,600. Check: SP₁ = 2,000 and SP₂ = 1,920.
Answer: ₹1,600
60-Second Revision
- Gain % at CP = (charged quantity − given quantity)/given quantity × 100.
- Weight short by e%: gain = e/(100 − e) × 100; 900 g for 1 kg = 11 1/9%.
- Mark-up plus false weight: [(1 + m/100) × true/false − 1] × 100.
- Takes x% extra, gives y% less: [(100 + x)/(100 − y) − 1] × 100; a bare "cheats x% both ways" is keyed as (1 + x/100)² − 1.
- Water w per milk m at CP of milk: w/m × 100; p% on SP = [p/(100 − p)] × 100 on CP.