A man sold 400 chairs and had a gain equal to selling price of 50 chairs. What is his profit percentage?

Options

A. `14.28`
B. 25
C. `11.11`
D. 10

Answer

To solve the problem step by step, we need to find the profit percentage based on the information given.

### Step 1: Define the Selling Price of One Chair
Let the selling price of one chair be \( SP \). According to the problem, we can assume \( SP = Rs.100 \) for simplicity.

### Step 2: Calculate the Total Selling Price for 400 Chairs
The total selling price for 400 chairs can be calculated as:
\[ \text{Total Selling Price} = 400 \times SP = 400 \times 100 = Rs.40,000 \]

### Step 3: Determine the Profit
The problem states that the gain (profit) is equal to the selling price of 50 chairs. Therefore, we calculate the profit as:
\[ \text{Profit} = 50 \times SP = 50 \times 100 = Rs.5,000 \]

### Step 4: Calculate the Cost Price
The cost price (CP) can be found using the formula:
\[ \text{Cost Price} = \text{Total Selling Price} - \text{Profit} \]
Substituting the values we have:
\[ CP = 40,000 - 5,000 = Rs.35,000 \]

### Step 5: Calculate the Profit Percentage
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{5,000}{35,000} \right) \times 100 \]
Calculating this gives:
\[ \text{Profit Percentage} = \left( \frac{5}{35} \right) \times 100 = \frac{1}{7} \times 100 \approx 14.29\% \]

### Final Answer
The profit percentage is approximately **14.29%**.

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