A dishonest shopkeeper sells goods at cost price but uses a false weight of 875 grams in place of 1 kg. Find his profit percentage.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(14\frac{2}{7}\%\)
He charges for 1000 g but gives only 875 g, so he gains the cost of 125 g on goods costing him 875 g.
Gain on each sale \(=1000-875=125\) g
Profit percentage \(\displaystyle =\frac{125}{875}\times100=14\frac{2}{7}\%\)
His profit is \(14\frac{2}{7}\%\).
Why the other options are incorrect
Option (1) \(114\frac{2}{7}\%\) — Incorrect. This is the price received as a percentage of the cost of 875 g, not the gain.
Option (2) 87.5% — Incorrect. This is the weight given, 875 g, as a percentage of 1 kg, not the profit.
Option (4) 12.5% — Incorrect. This divides the 125 g saved by 1000 g; the gain is on what he actually gives, 875 g.