Question

A man marks his goods at a price that would give him 20% profit. He sells \( \frac{3}{5} \) of the goods at the marked price and sells the remaining at 20% discount. The gain percent in the whole transaction is:

• A. 10%
• B. 12%
• C. 10.4%
• D. 15%

Hint:

For problems involving selling at a profit and a discount, split the total goods into parts, calculate each part’s profit or loss, then find the total gain.

Answer 1

The Correct Option is C

Let the cost price of the total goods be \( C \) and the marked price be \( M \). 
Step 1: The selling price of \( \frac{3}{5} \) of the goods at marked price is: \[ \text{Selling Price 1} = \frac{3}{5}M \] The cost price for these goods is \( \frac{3}{5}C \), and the profit for this part is: \[ \text{Profit 1} = \frac{3}{5}M - \frac{3}{5}C \] Since the profit margin is 20\%, we have: \[ M = 1.2 \times \frac{3}{5}C \] 
Step 2: The remaining \( \frac{2}{5} \) of the goods is sold at 20\% discount, so the selling price for these goods is: \[ \text{Selling Price 2} = \frac{2}{5}M \times 0.8 = \frac{2}{5} \times 0.8M = \frac{4}{25}M \] 
Step 3: The total selling price is: \[ \text{Total Selling Price} = \frac{3}{5}M + \frac{4}{25}M = \frac{19}{25}M \] The total cost price is \( C \), and we can now find the total profit: \[ \text{Total Profit} = \text{Total Selling Price} - C = \frac{19}{25}M - C \] 
Step 4: Solve for the total gain percentage: \[ \text{Gain Percentage} = \frac{\text{Total Profit}}{C} \times 100 = 10.4\% \] Thus, the gain percent in the whole transaction is 10.4%.