A merchant purchases a watch for Rs. 510 and fixes its marked price in such a way that after allowing a discount of 15%, he earns a profit of 30%. What is the marked price (in Rs.) of the watch ?

Options

A. 650
B. 690
C. 780
D. 730

Answer

To solve the problem step by step, we need to determine the marked price (MP) of the watch based on the given cost price (CP), discount percentage, and profit percentage.

### Step 1: Understand the given values
- Cost Price (CP) = Rs. 510
- Discount = 15%
- Profit = 30%

### Step 2: Calculate the Selling Price (SP)
To find the Selling Price (SP) when a profit of 30% is made, we can use the formula:
\[ SP = CP + \text{Profit} \]
The profit can be calculated as:
\[ \text{Profit} = \frac{30}{100} \times CP = \frac{30}{100} \times 510 = 153 \]
Now, substituting the profit back into the SP formula:
\[ SP = 510 + 153 = 663 \]

### Step 3: Relate Selling Price to Marked Price
The Selling Price (SP) is also related to the Marked Price (MP) through the discount. The formula for SP when a discount is applied is:
\[ SP = MP - \text{Discount} \]
The discount can be calculated as:
\[ \text{Discount} = \frac{15}{100} \times MP = 0.15 \times MP \]
Thus, we can express SP in terms of MP:
\[ SP = MP - 0.15 \times MP = 0.85 \times MP \]

### Step 4: Set up the equation
Now we can set the two expressions for SP equal to each other:
\[ 663 = 0.85 \times MP \]

### Step 5: Solve for Marked Price (MP)
To find MP, we rearrange the equation:
\[ MP = \frac{663}{0.85} \]
Calculating this gives:
\[ MP = 780 \]

### Conclusion
The marked price of the watch is Rs. 780.