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Dishonest Dealer Problems: Profit from False Weights

Gain at cost price • False weight plus profit • False weight with loss • Cheating both ways

SSC Banking 📅 Last updated: 2026-10-20

In a false-weight question the dealer charges the customer for one quantity but hands over less. The extra money is pure gain, but it must be measured against what the dealer actually gave away, because that is his real cost. This one idea, cost is what is delivered, settles almost every variation.

The cleanest way to work is with a ratio. Write what the customer pays as a multiple of cost, multiply by the quantity charged for, divide by the quantity delivered, and subtract 1.

Overall gain = (price factor) × (claimed quantity ÷ actual quantity) − 1, where the price factor is 1 at cost price, 1.1 at a 10% profit, 0.95 at a 5% loss, and so on.

With a price factor of 1, the formula reduces to the familiar version: gain% = (error ÷ false weight) × 100, where the error is the true weight minus the false weight.

Worked example 1: a 900 g "kilogram"

The dealer gives 900 g but charges for 1,000 g. Error = 100 g. Gain = 100 ÷ 900 × 100 = 11.11%, not 10%.

The trap answer of 10% comes from dividing by 1,000 g, which measures the loss to the customer rather than the dealer's gain on cost. Exam options nearly always include it.

Worked example 2: finding the false weight

A dealer claims to sell at cost but gains 25%. The real quantity × 1.25 must equal the 1,000 g he charges for, so he gives 1,000 ÷ 1.25 = 800 g.

When the dealer also adds a profit, or even announces a loss, multiply the two effects; do not add them. Each acts on the price per gram the customer really pays.

Worked example 3: 10% profit and an 800 g weight

Overall factor = 1.1 × 1,000/800 = 1.375, so the total gain is 37.5%. Adding 10% and 25% would give 35%, which is wrong.

Worked example 4: a "loss" that is really a gain

A dealer announces a 4% loss but uses an 840 g weight. Overall factor = 0.96 × 1,000/840 ≈ 1.1429, a real gain of about 14.29%.

The same structure works backwards. To reach a target overall gain with a known false weight, divide the target factor by the weight ratio to get the mark-up you need.

Some dealers cheat their suppliers too, taking more than they pay for. Treat both stages as quantity ratios and multiply them.

Worked example 5: 10% each way

When buying, the dealer takes 1,100 g for the price of 1 kg. When selling, he gives 900 g for the price of 1 kg. So the goods he paid 1 kg's price for are sold as 1,100/900 kg. Gain = 1,100/900 − 1 ≈ 22.22%.

Adulteration questions use the same logic. If a milkman mixes water equal to one-fifth of the milk and sells the mixture at the cost price of milk, he sells 1.2 litres for every litre he paid for.

Worked example 6: water in milk

Milk 1 litre + water 0.2 litres, all sold at the price of milk. Gain = 0.2 ÷ 1 = 20%. The water's share of the mixture (1/6) is not the gain; the gain is water ÷ milk.

If a ratio answer feels uncertain, put in a price and follow the money. This takes longer than the formula but catches the commonest mistake, which is dividing by the wrong quantity.

Worked example 7: a 900 g weight at ₹50 a kg

The dealer pays ₹50 a kg, so the 900 g he hands over cost him ₹45. The customer pays ₹50, the price of a full kilogram. Gain = ₹5 on a cost of ₹45, which is 11.11%, matching worked example 1.

The rupee check also makes clear why the stated price per kg never matters: change ₹50 to any other figure and both the cost and the revenue scale together, leaving the percentage unchanged.

  • ✘ Dividing the error by the true weight instead of the false weight.
  • ✘ Adding the false-weight gain to a stated profit instead of multiplying the factors.
  • ✘ Reading "sells at a loss" as a real loss without checking the weight.
  • ✘ In adulteration questions, dividing by the mixture instead of by the pure quantity.
Dealer gives for 1 kgGain at cost price
950 g5.26%
900 g11.11%
875 g14.29%
800 g25%
750 g33.33%

False-weight questions are profit and loss with a quantity twist. For related techniques see successive discounts and alligation for mixtures, or the Quant cheat code.

Q1. A shopkeeper sells at cost price but uses a 960 g weight in place of 1 kg. What is his gain percentage? easy

✅ Answer: (a) 4.17%

💡 Explanation: He gains 40 g on every 960 g he actually gives. Gain = 40 ÷ 960 × 100 = 4.17%. Dividing by 1,000 instead gives the trap answer of 4%.

Q2. A trader marks a 20% profit and also uses a 900 g weight for 1 kg. What is his total gain? medium

✅ Answer: (c) 33.33%

💡 Explanation: He charges 1.2 times the cost of 1,000 g while giving 900 g. Gain = 1.2 × 1,000/900 − 1 = 1/3, i.e. 33.33%.

Q3. A dealer claims to sell at a 10% loss but uses a 750 g weight for 1 kg. What is the actual result? medium

✅ Answer: (b) 20% gain

💡 Explanation: He charges 0.9 times the cost of 1,000 g for 750 g. Gain = 0.9 × 1,000/750 − 1 = 0.2, a 20% gain.

Q4. A merchant claims to sell at cost price but makes a 20% profit by using a false weight. What does he give for 1 kg? medium

✅ Answer: (d) 833.33 g

💡 Explanation: The gain is 20% on what he actually gives, so the true quantity × 1.2 = 1,000 g, giving 833.33 g. Subtracting 20% of 1 kg (800 g) is a common error.

Q5. A trader cheats by 20% when buying, taking 1,200 g for the price of 1 kg, and by 20% when selling, giving 800 g for 1 kg. What is his gain if he buys and sells at the same price per kg? hard

✅ Answer: (a) 50%

💡 Explanation: For the cost of 1 kg he receives 1,200 g. He then sells it in 800 g lots, each charged as a full kg, so revenue ÷ cost = 1,200 ÷ 800 = 1.5, a 50% gain.

Q6. A shopkeeper uses a 900 g weight for 1 kg and wants an overall gain of 25%. By what percentage above cost should he price his goods? hard

✅ Answer: (b) 12.5%

💡 Explanation: If the mark-up is m, then (1 + m) × 1,000/900 = 1.25, so 1 + m = 1.25 × 0.9 = 1.125 and m = 12.5%.

Why do I divide by the false weight and not by 1 kg?

Profit percentage is measured against cost. The dealer's real cost is the goods he actually hands over, the false weight, while he is paid for the full kilogram. So the gain is the missing amount divided by what he gives, not by what he claims to give.

Does the answer change if the price per kg is not given?

No. Profit percentage depends only on the ratio of what is paid to what is delivered. You can assume any price per kg, such as ₹1 or ₹100 per gram, and the percentage comes out the same.

All problems and solutions on this page are original. No outside facts are relied on; every numeric answer is recomputed by software before publishing.

How this page was prepared. Drafted with AI assistance (Claude (Anthropic AI model)) from the sources listed above. 13 calculations on this page were recomputed by software and matched. Automated checks also covered structure, internal links and duplicate text. Software checks cannot confirm facts. Reviewed by praveen on 2026-10-20 against the sources listed above.

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