By selling a fan for Rs. 2604 there is a loss of `7%`. If it is sold for Rs. 3094, then the profit percentage is

Options

A. `10%`
B. `12%`
C. `9.5%`
D. `10.5%`

Answer

To solve the problem step by step, we need to find the cost price (CP) of the fan first and then calculate the profit percentage when it is sold for Rs. 3094.

### Step 1: Find the Cost Price (CP)
Given that selling the fan for Rs. 2604 results in a loss of 7%, we can use the formula for loss:

\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} - \text{Loss} \]

We can express the loss in terms of the cost price:

\[ \text{Loss} = \frac{7}{100} \times \text{CP} \]

Substituting the values into the loss formula:

\[ 2604 = \text{CP} - \frac{7}{100} \times \text{CP} \]

This can be rewritten as:

\[ 2604 = \text{CP} \left(1 - \frac{7}{100}\right) \]

Calculating \(1 - \frac{7}{100}\):

\[ 1 - \frac{7}{100} = \frac{93}{100} \]

So we have:

\[ 2604 = \text{CP} \times \frac{93}{100} \]

Now, solving for CP:

\[ \text{CP} = \frac{2604 \times 100}{93} \]

Calculating this gives:

\[ \text{CP} = \frac{260400}{93} \approx 2800 \]

### Step 2: Calculate the Profit when Sold for Rs. 3094
Now that we have the cost price, we can find the profit when the fan is sold for Rs. 3094.

\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]

Substituting the values:

\[ \text{Profit} = 3094 - 2800 = 294 \]

### Step 3: Calculate the Profit Percentage
The profit percentage can be calculated using the formula:

\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \]

Substituting the values:

\[ \text{Profit Percentage} = \left(\frac{294}{2800}\right) \times 100 \]

Calculating this gives:

\[ \text{Profit Percentage} = \left(0.105\right) \times 100 = 10.5\% \]

### Final Answer
The profit percentage when the fan is sold for Rs. 3094 is **10.5%**.