Umang sells 250 apples then he gets profit equal to sell price of 50 apples. What is his profit in percentage?

Options

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

Answer

To solve the problem step by step, let's break it down:

1. **Understanding the Problem**:
- Umang sells 250 apples.
- The profit he makes is equal to the selling price of 50 apples.

2. **Assuming Selling Price**:
- Let's assume the selling price of 1 apple is \( S \) rupees.
- Therefore, the selling price of 250 apples is \( 250S \).
- The profit is equal to the selling price of 50 apples, which is \( 50S \).

3. **Calculating Profit**:
- Profit = Selling Price - Cost Price
- From the information given, we know that:
\[ \text{Profit} = 50S \]
- Therefore, we can express the cost price (CP) in terms of selling price (SP):
\[ \text{Cost Price} = \text{Selling Price} - \text{Profit} = 250S - 50S = 200S \]

4. **Calculating Profit Percentage**:
- 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:
\[ \text{Profit Percentage} = \left( \frac{50S}{200S} \right) \times 100 \]
- Simplifying this:
\[ \text{Profit Percentage} = \left( \frac{50}{200} \right) \times 100 = \frac{1}{4} \times 100 = 25\% \]

5. **Conclusion**:
- Thus, the profit percentage is 25%.