A dealer purchsed a fan for Rs. 1080. After allowing a discount of 25% on its marked price.he gains 25%. Find the marked price of the fan.

Answer

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

### Step 1: Understand the given information
- Cost Price (CP) of the fan = Rs. 1080
- Discount = 25% on the marked price (MP)
- Gain = 25%

### Step 2: Calculate the Selling Price (SP)
Since the dealer gains 25%, we can calculate the Selling Price using the formula:
\[ \text{SP} = \text{CP} + \text{Gain} \]
Where Gain is calculated as:
\[ \text{Gain} = \frac{25}{100} \times \text{CP} \]
So,
\[ \text{Gain} = \frac{25}{100} \times 1080 = 270 \]
Now, we can find the Selling Price:
\[ \text{SP} = 1080 + 270 = 1350 \]

### Step 3: Relate Selling Price to Marked Price
The Selling Price is also related to the Marked Price through the discount given. The Selling Price after a discount of 25% on the Marked Price can be expressed as:
\[ \text{SP} = \text{MP} - \text{Discount} \]
Where Discount can be calculated as:
\[ \text{Discount} = \frac{25}{100} \times \text{MP} = 0.25 \times \text{MP} \]
Thus, we can rewrite the Selling Price equation as:
\[ \text{SP} = \text{MP} - 0.25 \times \text{MP} \]
This simplifies to:
\[ \text{SP} = 0.75 \times \text{MP} \]

### Step 4: Substitute the Selling Price into the equation
Now we can substitute the Selling Price we calculated:
\[ 1350 = 0.75 \times \text{MP} \]

### Step 5: Solve for Marked Price
To find the Marked Price, we can rearrange the equation:
\[ \text{MP} = \frac{1350}{0.75} \]
Calculating this gives:
\[ \text{MP} = 1800 \]

### Conclusion
The marked price of the fan is Rs. 1800.

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