On selling 56 chairs. Mohan earns profit equal to the selling the price of 6 chairs. what is the profit per cent ?

Options

A. 9.28
B. 10.71
C. 12
D. 13.7

Answer

To solve the problem step-by-step, we will follow the information provided in the question and apply the formulas related to profit and loss.

### Step 1: Understand the Given Information
Mohan sells 56 chairs and earns a profit equal to the selling price of 6 chairs.

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

### Step 3: Express Profit in Terms of SP and CP
The profit can be expressed as:
\[ \text{Profit} = \text{SP of 56 chairs} - \text{CP of 56 chairs} \]
This can be written as:
\[ \text{Profit} = 56 \times SP - 56 \times CP \]

### Step 4: Set Up the Equation
According to the problem, the profit is equal to the selling price of 6 chairs:
\[ \text{Profit} = 6 \times SP \]
Thus, we can set up the equation:
\[ 56 \times SP - 56 \times CP = 6 \times SP \]

### Step 5: Rearrange the Equation
Rearranging the equation gives us:
\[ 56 \times SP - 6 \times SP = 56 \times CP \]
\[ 50 \times SP = 56 \times CP \]

### Step 6: Solve for SP in Terms of CP
From the equation \( 50 \times SP = 56 \times CP \), we can express SP in terms of CP:
\[ SP = \frac{56}{50} \times CP \]
\[ SP = 1.12 \times CP \]

### Step 7: Calculate the Profit
The profit per chair can be calculated as:
\[ \text{Profit} = SP - CP \]
Substituting the value of SP:
\[ \text{Profit} = (1.12 \times CP) - CP \]
\[ \text{Profit} = 0.12 \times CP \]

### Step 8: Calculate the Profit Percentage
Profit percentage is given by:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the profit:
\[ \text{Profit Percentage} = \left( \frac{0.12 \times CP}{CP} \right) \times 100 \]
\[ \text{Profit Percentage} = 0.12 \times 100 \]
\[ \text{Profit Percentage} = 12\% \]

### Final Answer
The profit percentage is **12%**.

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