A man sold 250 chairs and had a gain equal to selling price of 50 chairs. What is his profit percentage

Options

A. 20
B. 25
C. 10
D. 15

Answer

To solve the problem step by step, we can follow these calculations:

1. **Understand the given information**:
- The man sold 250 chairs.
- The gain (profit) he made is equal to the selling price of 50 chairs.

2. **Let’s denote the selling price of one chair**:
- Let the selling price (SP) of one chair be \( SP \).

3. **Calculate the total selling price of 250 chairs**:
- Total Selling Price (TSP) = Number of chairs sold × Selling Price per chair
- \( TSP = 250 \times SP \)

4. **Calculate the profit**:
- The profit is equal to the selling price of 50 chairs.
- Profit = Selling Price of 50 chairs = \( 50 \times SP \)

5. **Now, we can find the cost price (CP)**:
- We know that Profit = Total Selling Price - Cost Price
- Therefore, we can write:
\[ Profit = TSP - CP \]
\[ 50 \times SP = (250 \times SP) - CP \]
\[ CP = (250 \times SP) - (50 \times SP) \]
\[ CP = 200 \times SP \]

6. **Now, we can calculate the profit percentage**:
- Profit Percentage = \( \frac{Profit}{CP} \times 100 \)
- Substitute the values we have:
\[ Profit Percentage = \frac{50 \times SP}{200 \times SP} \times 100 \]
- The \( SP \) cancels out:
\[ Profit Percentage = \frac{50}{200} \times 100 \]
\[ Profit Percentage = \frac{1}{4} \times 100 = 25\% \]

Thus, the profit percentage is **25%**.