Profit and Loss Question 1 - CAT 2023
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:
Step-by-Step Explanation
- Analyze the Purchase (Merchant's Cost):
The merchant pays Rs. 100 for every 100 cm but actually gets 105 cm.
Cost Price (CP) of 105 cm = Rs. 100
- Analyze the Sale (Merchant's Revenue):
The baseline selling price is set at Rs. 110 per meter (100 cm).
A 5% discount is offered on this price:
Discounted price for a 100 cm transaction = 110 × 0.95 = Rs. 104.5
However, the merchant cheats the customer by delivering only 95 cm instead of 100 cm. Therefore, the merchant receives Rs. 104.5 for every 95 cm he gives away.
Selling Price (SP) of 95 cm = Rs. 104.5
- Equate Quantities to Find Profit:
Calculate the selling price per centimeter:
SP per cm = 104.5 / 95 = Rs. 1.1
Since the merchant actually possesses 105 cm of cloth for every Rs. 100 spent, his total revenue from selling this entire stock is:
Total SP for 105 cm = 105 × 1.1 = Rs. 115.5
Profit Percentage = (115.5 − 100) / 100 × 100 = 15.5%
Correct Option: C
💡 FundaMakers Tip:
For problems involving dishonest dealers or complex units, use the Price per Unit Quantity approach. Break the transaction down to finding the effective CP per unit and SP per unit.
Effective CP per cm = 100 / 105 and Effective SP per cm = 104.5 / 95.
The net profit factor is simply:
Effective SP / Effective CP = (104.5 / 95) × (105 / 100) = 1.155, directly yielding a 15.5% profit. This workflow avoids confusion regarding weights and measures.