Numerical answer
A trader marks his goods 40% above cost price and allows a discount of 15% on the marked price. In addition, he uses a false weight that measures 850 g when it should measure 1 kg. What is his overall profit percentage?
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Answer: 40
Let the cost price be ₹C per kg.
Marked price = 1.4C per kg; selling price after 15% discount = 1.4C × 0.85 = 1.19C for what the customer believes is 1 kg.
But the customer actually receives only 850 g, which costs the trader 0.85C.
Profit % = (1.19C − 0.85C)/0.85C × 100 = (1.19/0.85 − 1) × 100 = (1.4 − 1) × 100 = 40%.
Tip: with a false weight, profit factor = (selling-price factor)/(fraction of true weight given).
Marked price = 1.4C per kg; selling price after 15% discount = 1.4C × 0.85 = 1.19C for what the customer believes is 1 kg.
But the customer actually receives only 850 g, which costs the trader 0.85C.
Profit % = (1.19C − 0.85C)/0.85C × 100 = (1.19/0.85 − 1) × 100 = (1.4 − 1) × 100 = 40%.
Tip: with a false weight, profit factor = (selling-price factor)/(fraction of true weight given).
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