A cloth merchant sold half of his cloth at 40% profit, half of re maining at 40% loss and the rest was sold at the cost price. In the total transaction his gain or loss will be

Options

A. 20%gain
B. 25%loss
C. 10%gain
D. 15%loss

Answer

To solve the problem step by step, we will assume the total cost price of the cloth is 100 units. This will make our calculations easier.

### Step 1: Determine the total cost price
Assume the total cost price (CP) of the cloth is 100.

### Step 2: Calculate the selling price for the first half sold at 40% profit
- The merchant sold half of his cloth, which is \( \frac{100}{2} = 50 \) units.
- Selling price (SP) for this half at 40% profit:
\[ \text{Profit} = 40\% \text{ of } 50 = \frac{40}{100} \times 50 = 20 \]
\[ \text{SP} = \text{CP} + \text{Profit} = 50 + 20 = 70 \]

### Step 3: Calculate the selling price for the second half sold at 40% loss
- The remaining cloth after selling the first half is also 50 units.
- Half of the remaining cloth is sold, which is \( \frac{50}{2} = 25 \) units.
- Selling price (SP) for this half at 40% loss:
\[ \text{Loss} = 40\% \text{ of } 25 = \frac{40}{100} \times 25 = 10 \]
\[ \text{SP} = \text{CP} - \text{Loss} = 25 - 10 = 15 \]

### Step 4: Calculate the selling price for the remaining cloth sold at cost price
- The remaining cloth after selling the first 25 units is also 25 units.
- This remaining cloth is sold at cost price, so:
\[ \text{SP} = \text{CP} = 25 \]

### Step 5: Calculate the total selling price
- Now, add up all the selling prices:
\[ \text{Total SP} = 70 + 15 + 25 = 110 \]

### Step 6: Calculate the total profit or loss
- The total cost price was 100, and the total selling price is 110.
- Therefore, the profit can be calculated as:
\[ \text{Profit} = \text{Total SP} - \text{Total CP} = 110 - 100 = 10 \]

### Step 7: Calculate the percentage profit
- The percentage profit can be calculated as:
\[ \text{Percentage Profit} = \left(\frac{\text{Profit}}{\text{Total CP}}\right) \times 100 = \left(\frac{10}{100}\right) \times 100 = 10\% \]

### Final Answer:
The merchant made a profit of **10%**.

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