A trader claims to sell millet at a profit of 61%, but also dishonestly uses a…
2025
A trader claims to sell millet at a profit of 61%, but also dishonestly uses a weight that is 2% less than what is mentioned on it. Find the total percentage of profit earned by the trader. (Round the answer to the nearest whole number.)
- A.
59%
- B.
64%
- C.
67%
- D.
63%
Attempted by 6 students.
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Correct answer: B
When a trader marks up goods by a claimed profit percentage but also hands over a weight lighter than what is stated on it, the real profit is higher than the claimed figure. The two effects must be combined by working out the profit on the cost of what is actually supplied (the smaller, true quantity), not on the cost of the quantity that was billed to the customer.
Assume the cost price of 100 units (the labelled weight) is ₹100, so the cost per unit is ₹1.
At a claimed profit of 61%, the trader bills the customer ₹100 × 1.61 = ₹161 for the 100 labelled units.
Since the weight actually used is 2% less than what is stated, the customer receives only 100 − 2 = 98 units.
The trader's real cost for the 98 units actually supplied is 98 × ₹1 = ₹98.
Actual profit = Revenue − Real cost = ₹161 − ₹98 = ₹63.
Actual profit percentage = (63 ÷ 98) × 100 = 64.28…%, which rounds to 64%.
This matches the general relation for a claimed profit p% combined with a weight shortfall of c%: Total Profit% = [(100 + p) ÷ (100 − c) − 1] × 100. With p = 61 and c = 2: [(161) ÷ 98 − 1] × 100 = (63 ÷ 98) × 100 ≈ 64.29%, confirming the step-by-step result of 64%.