On selling 25 shirts, a retailer earns profit equal to the cost price of 8 shirts. What is the profit percentage?

Options

A. 47 .05
B. 32
C. 25
D. 34.5

Answer

To find the profit percentage when selling 25 shirts, where the profit equals the cost price of 8 shirts, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Cost Price (CP)**:
Let the cost price of one shirt be \( X \). Therefore, the cost price of 25 shirts will be:
\[ \text{CP of 25 shirts} = 25X \]

2. **Calculate the Profit**:
According to the problem, the profit earned from selling 25 shirts is equal to the cost price of 8 shirts. The cost price of 8 shirts is:
\[ \text{CP of 8 shirts} = 8X \]
Thus, the profit (P) is:
\[ P = 8X \]

3. **Determine the Selling Price (SP)**:
The selling price (SP) can be calculated by adding the profit to the cost price:
\[ \text{SP} = \text{CP} + \text{Profit} = 25X + 8X = 33X \]

4. **Calculate Profit Percentage**:
The profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{8X}{25X} \right) \times 100 \]

5. **Simplify the Expression**:
The \( X \) in the numerator and denominator cancels out:
\[ \text{Profit Percentage} = \left( \frac{8}{25} \right) \times 100 \]
Now, calculate \( \frac{8}{25} \):
\[ \frac{8}{25} = 0.32 \]
Therefore,
\[ \text{Profit Percentage} = 0.32 \times 100 = 32\% \]

### Final Answer:
The profit percentage is **32%**.