A dishonest dealer professes to sell his goods at Cost Price but still gets…
2025
A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
Attempted by 30 students.
Show answer & explanation
Key idea: the dealer charges the cost price for 1 kg but actually gives only w grams, so set up the profit equation and solve for w.
Step 1: Define variables.
Let C = cost of 1 kg (true cost).
Let w grams be the substituted weight used and sold as '1 kg'.
Step 2: Express selling price and actual cost of goods given.
Selling price for the labelled kilogram = C (he professes to sell at cost).
Actual cost of the w grams given = (w/1000)·C.
Step 3: Write the profit percent equation.
Profit% = (Selling price − Cost of goods given) / (Cost of goods given). So
(C − (w/1000)C) / ((w/1000)C) = 20% = 1/5.
Step 4: Solve for w.
Simplify the equation: (1 − w/1000) / (w/1000) = 1/5 ⇒ (1000 − w)/w = 1/5.
Cross-multiply: 1000 − w = w/5 ⇒ 1000 = w + w/5 = (6/5)w.
So w = 1000 · (5/6) = 5000/6 = 2500/3 grams = 833 1/3 grams.
Conclusion: The dealer substitutes 833 1/3 grams for a kilogram.