If the cost price of 50 oranges is equal to the selling price of 40 oranges, then the profit per cent is

Options

A. 5
B. 10
C. 20
D. 25

Answer

To solve the problem, we need to determine the profit percentage based on the given information about the cost price and selling price of oranges.

### Step-by-Step Solution:

1. **Define Variables:**
Let the cost price (CP) of 1 orange be \( x \).
Therefore, the cost price of 50 oranges will be \( 50x \).

2. **Selling Price Calculation:**
According to the problem, the selling price (SP) of 40 oranges is equal to the cost price of 50 oranges. Hence, we can write:
\[ SP \text{ of 40 oranges} = 50x \]

3. **Selling Price of One Orange:**
The selling price of 1 orange can be calculated as:
\[ SP \text{ of 1 orange} = \frac{SP \text{ of 40 oranges}}{40} = \frac{50x}{40} = \frac{5x}{4} \]

4. **Calculate Profit:**
The profit made on selling one orange can be calculated as:
\[ \text{Profit} = SP - CP = \frac{5x}{4} - x \]
To simplify this, we convert \( x \) to a fraction:
\[ \text{Profit} = \frac{5x}{4} - \frac{4x}{4} = \frac{5x - 4x}{4} = \frac{x}{4} \]

5. **Calculate Profit Percentage:**
The profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{\frac{x}{4}}{x} \right) \times 100 = \left( \frac{1}{4} \right) \times 100 = 25\% \]

### Final Answer:
The profit percentage is **25%**.