Numerical answer
A trader marks his goods 35% above the cost price and allows a discount of 10% on the marked price. In addition, he uses a faulty weight so that he hands over only 900 g when he claims to sell 1 kg. What is his overall profit percentage?
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Answer: 35
Let the cost price be ₹100 per kg.
Marked price = ₹135 per kg; after a 10% discount the selling price = 135 × 0.9 = ₹121.5 per 'kg'.
But the customer receives only 900 g, whose cost to the trader = ₹90.
Profit % = (121.5 − 90)/90 × 100 = 31.5/90 × 100 = 35%.
Tip: Overall multiplier = (1.35 × 0.9)/0.9 = 1.35 — since the discount factor (0.9) equals the weight-shortfall factor (900/1000 = 0.9), they cancel, leaving profit % equal to the markup %.
Marked price = ₹135 per kg; after a 10% discount the selling price = 135 × 0.9 = ₹121.5 per 'kg'.
But the customer receives only 900 g, whose cost to the trader = ₹90.
Profit % = (121.5 − 90)/90 × 100 = 31.5/90 × 100 = 35%.
Tip: Overall multiplier = (1.35 × 0.9)/0.9 = 1.35 — since the discount factor (0.9) equals the weight-shortfall factor (900/1000 = 0.9), they cancel, leaving profit % equal to the markup %.
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