A merchant purchases a watch for Rs 540 and fixes its marked price in such a way that after allowing a discount of `10%` , he earns a profit of `35%` . What is the marked price (in Rs) of the watch?

Options

A. 790
B. 810
C. 750
D. 840

Answer

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

### Step 1: Understand the given information
- Cost Price (CP) of the watch = Rs 540
- Profit Percentage = 35%
- Discount Percentage = 10%

### Step 2: Calculate the Selling Price (SP)
To find the selling price after the profit, we can use the formula:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
Where Profit can be calculated as:
\[ \text{Profit} = \text{Cost Price} \times \frac{\text{Profit Percentage}}{100} = 540 \times \frac{35}{100} = 189 \]
Thus,
\[ \text{Selling Price (SP)} = 540 + 189 = 729 \]

### Step 3: Relate Selling Price to Marked Price
The selling price is related to the marked price (MP) after applying the discount. The relationship can be expressed as:
\[ \text{SP} = \text{MP} \times \left(1 - \frac{\text{Discount Percentage}}{100}\right) \]
Substituting the known values:
\[ 729 = \text{MP} \times \left(1 - \frac{10}{100}\right) = \text{MP} \times 0.90 \]

### Step 4: Solve for Marked Price (MP)
To find the marked price, rearrange the equation:
\[ \text{MP} = \frac{729}{0.90} = 810 \]

### Conclusion
The marked price of the watch is Rs 810.

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