Profit, Loss & Discount • Topic 5 of 6

False Weights

A dishonest trader who "sells at cost price" but hands over less than the stated weight still makes a real profit, because the customer pays for the full unit while receiving only the short weight. When the goods are sold at cost price, the gain % = error / (true value − error) × 100, where error is the shortfall. Selling a claimed 1,000 g but delivering 900 g means error 100, true 1,000 ⇒ gain = 100/900 × 100 = 11.11% (which is 1/9 — note it is on the actual weight given, not the claimed weight). If the trader ALSO marks the goods up by a normal profit %, the two effects compound as multipliers: overall multiplier = (1 + markup/100) × (true/given). The standard CAT version uses a faulty balance reading short — recognise that the base for the gain is the SMALLER, actual quantity delivered, never the claimed quantity.

✅ Solved examples

1. A trader sells at cost price but uses a 900 g weight for a kilogram. Find the gain %.
Gain = error/(true − error) × 100 = 100/900 × 100 = 11.11% (= 1/9).
2. A grocer’s weight reads 1 kg but actually weighs 800 g; he sells at cost price. Gain %?
Error 200, true 1000 ⇒ 200/(1000 − 200) × 100 = 200/800 × 100 = 25%.
3. A shopkeeper marks up 20% AND gives only 900 g per claimed kg. Find the overall gain %.
Multiplier = 1.20 × (1000/900) = 1.20 × 1.1111 = 1.3333 ⇒ 33.33% gain.
4. A dealer uses a weight of 960 g for 1 kg and sells at cost price. Gain %?
Error 40, true 1000 ⇒ 40/960 × 100 = 4.1667% ≈ 4.17%.

✏️ Practice — try these, take hints as needed

1. Sells at CP but delivers 950 g per claimed kg. Gain %?
error/(true − error).
50/(1000 − 50).
50/950 × 100.
≈ 5.26% (1/19)
2. A weight of 750 g passes for 1 kg, sold at CP. Gain %?
Error 250.
250/(1000 − 250).
250/750 × 100.
33⅓%
3. Marks up 10% and gives 900 g per kg. Overall gain %?
Multiply the effects.
1.10 × (1000/900).
1.10 × 1.1111.
≈ 22.22%
4. Uses an 800 g weight for a kilo, sold at CP. Gain %?
Error 200.
200/800.
×100.
25%
5. A trader claims to sell at CP but gains 25% by short-weighing. How many grams per claimed kg?
error/(1000 − error) = 0.25.
error = 0.25(1000 − error).
Solve for given weight.
800 g delivered

📝 Topic test — 8 questions

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