A "dishonest dealer" question always hides the same trick — selling at cost price while secretly using a false weight, so the profit comes purely from the missing grams.
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Profit and loss percentage are always calculated on the COST price, never on the selling price.
📌 The core formulas
Profit % = (SP − CP) ÷ CP × 100. CP=₹200, SP=₹250 → profit = ₹50 → 25%.
Loss % = (CP − SP) ù CP × 100. CP=₹500, SP=₹450 → loss = ₹50 → 10%.
To find SP from CP and profit%: SP = CP × (1 + profit%/100). CP=₹400, profit 20% → SP=₹480.
✨ Worked example — finding CP
Given
SP=₹380, loss=5%
CP = SP ÷ (1 − loss%/100)
Answer
380 ÷ 0.95
CP = ₹400
Two discounts applied one after another are NOT the same as adding them together.
Olympiad trap: "20% and then 10% off" does NOT equal 30% off. Net discount = 20 + 10 − (20×10)/100 = 28%. The second discount applies to the already-reduced price.
📊 Worked example
| Step | Price |
|---|---|
| Marked price | ₹1000 |
| After 20% discount | ₹800 |
| After a further 10% discount | ₹720 (10% of ₹800, not ₹1000) |
A dealer who claims to sell "at cost price" but uses a lighter weight is still making a real profit — on the missing weight.
The trick: a dealer uses a 900 g weight instead of 1000 g, but sells at cost price. His actual profit % = (true weight − false weight) ÷ false weight × 100 = (1000−900)/900 × 100 ≈ 11.11%.
12 questions on profit, loss, discount and dishonest dealer problems.
