This profit-loss question seems quite common in CAT but also tricky with all the cheating and discounts. Can someone help?

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. 4.2%
B. 15.5%
C. 16%
D. 9.7%

A. 4.2%
B. 15.5%
C. 16%
D. 9.7%

V Ritik · Accepted Answer

These kinds of profit questions are popular in CAT because they combine discount, cheating, and unit confusion. It gets easier if you break it into parts and assume simple values.

Cost price = Rs.100 per meter
Merchant gets 5% extra cloth,  receives 105 cm for every 100 cm bought
He gives only 95 cm to customers for every meter sold
Also gives 5% discount on Rs.110,  effective selling price = Rs.104.5 per meter

So the merchant receives 104.5 &times; 100 &times; 105 and pays 95 &times; 100 &times; 100, which makes the profit ratio (104.5 &times; 100 &times; 105) &divide; (95 &times; 100 &times; 100) = 1.155. That means the profit is 15.5%. Answer is 15.5%, Option B. Keep the units in mind and cheat logic clear,  that&rsquo;s the key.

D. Aarav · Answer

These questions look tricky at first, but it helps to assume easy numbers. Say the merchant buys 95 meters of cloth at Rs.100 per meter. That means he pays Rs.9500. Since he gets 5% extra, he actually receives 95 &times; 1.05 = 99.75 meters of cloth. Now when he sells, he gives only 95 cm for every 1 meter the customer pays for,  so he cheats by giving just 0.95 meters per meter sold. The marked price is Rs.110, but he gives a 5% discount, so the effective selling price is Rs.104.5 per meter.
Now just calculate profit: total revenue = 104.5 &times; 100 &times; 105, and total cost = 95 &times; 100 &times; 100. That gives a profit ratio of 1.155, or 15.5%. So the correct answer is Option B.