On selling fan for ₹2585 a man gains `1/10` of its cost price. Find the cost price of the fan.

Options

A. Rs. 2550
B. Rs. 2450
C. Rs. 2350
D. Rs. 2650

Answer

To find the cost price of the fan, we can follow these steps:

### Step 1: Define the variables
Let the cost price of the fan be \( X \).

### Step 2: Understand the selling price and gain
The selling price (SP) of the fan is given as ₹2585. The gain is \( \frac{1}{10} \) of the cost price, which can be expressed as:
\[ \text{Gain} = \frac{1}{10} \times X \]

### Step 3: Set up the equation for gain
According to the formula for gain:
\[ \text{Gain} = \text{Selling Price} - \text{Cost Price} \]
We can substitute the known values into this equation:
\[ \frac{1}{10}X = 2585 - X \]

### Step 4: Rearrange the equation
To solve for \( X \), we first add \( X \) to both sides:
\[ \frac{1}{10}X + X = 2585 \]
This can be rewritten as:
\[ \frac{1}{10}X + \frac{10}{10}X = 2585 \]
Combining the terms gives:
\[ \frac{11}{10}X = 2585 \]

### Step 5: Solve for \( X \)
To isolate \( X \), multiply both sides by \( \frac{10}{11} \):
\[ X = 2585 \times \frac{10}{11} \]

### Step 6: Calculate the cost price
Now, we perform the multiplication:
\[ X = \frac{25850}{11} \]
Calculating this gives:
\[ X = 2350 \]

### Conclusion
The cost price of the fan is ₹2350.

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