Question:
A merchant purchases a cloth at a rate of Rs. 100 per meter and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs.110 per meter but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is
A merchant purchases a cloth at a rate of Rs. 100 per meter and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs.110 per meter but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is
Updated On: Nov 12, 2025
- 9.7%
- 16%
- 4.2%
- 15.5%
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The Correct Option is D
Solution and Explanation
To determine the merchant's profit percentage, follow these steps:
Step 1: Calculate the Effective Purchase Cost
For every 100 cm (1 meter) of cloth purchased, the merchant receives an additional 5 cm for free. Therefore, the total length of cloth received for 100 cm paid is 105 cm.
Thus, the effective cost per cm = Rs. 100/105 = Rs. 0.9524/cm.
Step 2: Calculate the Selling Price per cm
The merchant sells at Rs. 110 per meter (or 100 cm). So, the selling price per cm = Rs. 110/100 = Rs. 1.1/cm.
However, he cheats the customers by giving only 95 cm for every 100 cm paid for. Therefore, the effective selling price per cm is Rs. 1.1 * (100/95) = Rs. 1.1579/cm.
Step 3: Apply the Discount
The merchant offers a 5% discount on the selling price. The discounted selling price per cm = Rs. 1.1579 * 0.95 = Rs. 1.100005/cm.
Step 4: Calculate the Profit Percentage
Profit per cm = Selling price per cm - Cost price per cm = Rs. 1.100005 - Rs. 0.9524 = Rs. 0.147605.
Profit percentage = (Profit per cm/Cost price per cm) * 100 = (0.147605/0.9524) * 100 ≈ 15.5%.
Thus, the merchant's profit percentage is 15.5%.
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