Question

A trader buys 240 watches for ` 50,400 and he marks each of them at ` 320. He gives a discount of 15% on each watch and gives 1 watch free on a purchase of 5 watches. What is his minimum possible overall percentage of profit?

• A. 0.059
• B. 0.061
• C. 0.066
• D. 0.072
• E. 0.079

Answer 1

Answer: (E)

Step 1: Understand the problem.
A trader buys 240 watches for Rs. 50,400, and marks each of them at Rs. 320. He gives a discount of 15% on each watch and offers 1 free watch on the purchase of 5 watches. We need to calculate his minimum possible overall percentage of profit.

Step 2: Calculate the cost price per watch.
The total cost price for 240 watches is Rs. 50,400. The cost price per watch is: \[ \text{Cost price per watch} = \frac{50,400}{240} = 210 \] So, the cost price of each watch is Rs. 210.

Step 3: Calculate the selling price after the discount.
The trader gives a 15% discount on the marked price of Rs. 320. The selling price per watch after the discount is: \[ \text{Selling price} = 320 \times (1 - 0.15) = 320 \times 0.85 = 272 \] So, the selling price per watch after the discount is Rs. 272.

Step 4: Calculate the effective number of watches sold.
The trader gives 1 watch free on the purchase of 5 watches. For every 5 watches purchased, the customer gets 1 free watch, meaning that for every 5 paid watches, 6 watches are effectively given to the customer.
The total number of watches sold effectively is the total number of watches purchased divided by 5 (since 1 in every 5 watches is free): \[ \text{Total effective number of watches sold} = \frac{240}{5} \times 6 = 48 \times 6 = 288 \] So, the trader sells 288 watches effectively.

Step 5: Calculate the total revenue.
The total revenue is the selling price per watch multiplied by the total effective number of watches sold: \[ \text{Total revenue} = 272 \times 288 = 78336 \] So, the total revenue from selling the watches is Rs. 78,336.

Step 6: Calculate the total profit.
The total profit is the total revenue minus the total cost price: \[ \text{Total profit} = 78336 - 50400 = 27936 \] So, the total profit is Rs. 27,936.

Step 7: Calculate the percentage of profit.
The overall profit percentage is given by: \[ \text{Profit percentage} = \frac{\text{Total profit}}{\text{Total cost price}} \times 100 = \frac{27936}{50400} \times 100 \approx 0.079 \] Therefore, the minimum possible overall percentage of profit is 0.079%.

Step 8: Conclusion.
The minimum possible overall percentage of profit is 0.079%.

Final Answer:
The correct answer is (E): 0.079.