If the profit made by a merchant onselling 45 m of cloth is equal to the selling price of 5m of cloth, then his profit percentage is:

Options

A. `9.09%`
B. `12.5%`
C. `11.11%`
D. `10%`

Answer

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

### Step 1: Understand the given information
We know that the profit made by the merchant on selling 45 meters of cloth is equal to the selling price of 5 meters of cloth.

### Step 2: Define variables
Let:
- \( SP \) = Selling Price of 1 meter of cloth
- \( CP \) = Cost Price of 1 meter of cloth
- Profit from selling 45 meters = Selling Price of 5 meters

### Step 3: Write the equations
The selling price of 45 meters of cloth can be expressed as:
\[ SP_{45} = 45 \times SP \]

The selling price of 5 meters of cloth is:
\[ SP_{5} = 5 \times SP \]

According to the problem, the profit from selling 45 meters is equal to the selling price of 5 meters:
\[ SP_{45} - CP_{45} = SP_{5} \]
Where \( CP_{45} = 45 \times CP \).

### Step 4: Substitute and simplify
Substituting the expressions for \( SP_{45} \) and \( SP_{5} \):
\[ (45 \times SP) - (45 \times CP) = 5 \times SP \]

### Step 5: Rearrange the equation
Rearranging gives:
\[ 45SP - 45CP = 5SP \]
\[ 45SP - 5SP = 45CP \]
\[ 40SP = 45CP \]

### Step 6: Solve for SP in terms of CP
Dividing both sides by 5:
\[ 8SP = 9CP \]
Thus,
\[ SP = \frac{9}{8}CP \]

### Step 7: Calculate the profit
The profit made on selling 1 meter of cloth is:
\[ Profit = SP - CP = \frac{9}{8}CP - CP = \frac{9}{8}CP - \frac{8}{8}CP = \frac{1}{8}CP \]

### Step 8: Calculate the profit percentage
Profit percentage is given by:
\[ Profit\% = \left( \frac{Profit}{CP} \right) \times 100 \]
Substituting the profit:
\[ Profit\% = \left( \frac{\frac{1}{8}CP}{CP} \right) \times 100 = \frac{1}{8} \times 100 = 12.5\% \]

### Final Answer
The profit percentage is **12.5%**.

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