A merchant purchases a watch for Rs 560 and fixes its marked price in such a way that after allowing a discount of `20%`, he earns a profit of 40%. What is the marked price (in Rs) of the watch?

Options

A. 600
B. 980
C. 660
D. 750

Answer

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

### Step 1: Understand the Cost Price (CP) and Profit
The cost price (CP) of the watch is given as Rs 560. The merchant wants to earn a profit of 40%.

### Step 2: Calculate the Selling Price (SP)
To find the selling price (SP) that gives a 40% profit, we use the formula:
\[ SP = CP + \text{Profit} \]
Where profit is calculated as:
\[ \text{Profit} = \frac{40}{100} \times CP \]
So,
\[ \text{Profit} = \frac{40}{100} \times 560 = 224 \]
Thus,
\[ SP = 560 + 224 = 784 \]

### Step 3: Relate Selling Price to Marked Price and Discount
The selling price is also related to the marked price (MP) and the discount offered. The merchant offers a discount of 20% on the marked price. Therefore, we can express the selling price as:
\[ SP = MP - \text{Discount} \]
Where the discount is:
\[ \text{Discount} = \frac{20}{100} \times MP = 0.2 \times MP \]
Thus, we can rewrite the selling price as:
\[ SP = MP - 0.2 \times MP = 0.8 \times MP \]

### Step 4: Set Up the Equation
Now we can set up the equation using the selling price we calculated:
\[ 784 = 0.8 \times MP \]

### Step 5: Solve for Marked Price (MP)
To find the marked price, we rearrange the equation:
\[ MP = \frac{784}{0.8} \]
Calculating this gives:
\[ MP = 980 \]

### Conclusion
The marked price of the watch is Rs 980.

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