A man sold 250 chairs and had a gain equal to selling price of 50 chairs. His profit per cent is:

Options

A. 0.2
B. 0.25
C. 0.5
D. 0.15

Answer

To solve the problem step by step, let's break down the information given and apply the relevant formulas.

### Step 1: Understand the Problem
We know that a man sold 250 chairs and his gain (profit) is equal to the selling price of 50 chairs. We need to find the profit percentage.

### Step 2: Define Variables
Let:
- CP = Cost Price of one chair
- SP = Selling Price of one chair

### Step 3: Calculate Total Selling Price
The total selling price (SP) for 250 chairs can be expressed as:
\[ \text{Total SP} = 250 \times SP \]

### Step 4: Calculate Profit
According to the problem, the profit is equal to the selling price of 50 chairs:
\[ \text{Profit} = 50 \times SP \]

### Step 5: Use the Profit Formula
The profit can also be calculated using the formula:
\[ \text{Profit} = \text{Total SP} - \text{Total CP} \]
Where:
- Total CP = 250 × CP

So, we can write:
\[ 50 \times SP = (250 \times SP) - (250 \times CP) \]

### Step 6: Rearranging the Equation
Rearranging the equation gives:
\[ 250 \times CP = 250 \times SP - 50 \times SP \]
\[ 250 \times CP = 200 \times SP \]

### Step 7: Simplify the Equation
Dividing both sides by 50:
\[ 5 \times CP = 4 \times SP \]

### Step 8: Find the Ratio of SP to CP
Now, we can express the ratio of SP to CP:
\[ \frac{SP}{CP} = \frac{5}{4} \]

### Step 9: Calculate Profit
Using the profit formula:
\[ \text{Profit} = SP - CP \]
We can express it in terms of CP:
\[ SP = \frac{5}{4} \times CP \]
Thus,
\[ \text{Profit} = \frac{5}{4} \times CP - CP \]
\[ \text{Profit} = \left(\frac{5}{4} - 1\right) \times CP = \frac{1}{4} \times CP \]

### Step 10: Calculate Profit Percentage
Profit percentage is calculated as:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Total CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{\frac{1}{4} \times CP}{250 \times CP}\right) \times 100 \]
\[ \text{Profit Percentage} = \left(\frac{1}{1000}\right) \times 100 = 25\% \]

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

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