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. 9.7%
• B. 16%
• C. 4.2%
• D. 15.5%

Answer 1

The Correct Option is D

To determine the merchant's profit percentage, perform the following calculations:

Step 1: Determine the Effective Purchase Cost

For every 100 cm of cloth purchased, an additional 5 cm is received free, totaling 105 cm. The effective cost per cm is calculated as Rs. 100 / 105 = Rs. 0.9524/cm.

Step 2: Calculate the Selling Price per cm

The merchant sells cloth at Rs. 110 per meter (100 cm), resulting in a selling price of Rs. 110 / 100 = Rs. 1.1/cm. However, customers receive 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

A 5% discount is applied to the selling price. The discounted selling price per cm is Rs. 1.1579 * 0.95 = Rs. 1.100005/cm.

Step 4: Calculate the Profit Percentage

The profit per cm is the difference between the discounted selling price and the effective cost price: Rs. 1.100005 - Rs. 0.9524 = Rs. 0.147605.

The profit percentage is calculated as (Profit per cm / Cost price per cm) * 100 = (0.147605 / 0.9524) * 100, which is approximately 15.5%.

Consequently, the merchant's profit percentage is 15.5%.