A man purchased a watch for Rs. 400 and sold it at a gain of `20%` of the selling price. The selling price of the watch is -

Options

A. Rs. 300
B. Rs. 320
C. Rs. 440
D. Rs. 500

Answer

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

### Step 1: Understand the Given Information
The cost price (CP) of the watch is Rs. 400, and the profit is 20% of the selling price (SP).

### Step 2: Set Up the Equation
Let the selling price be denoted as \( X \). According to the problem, the profit is 20% of the selling price, which can be expressed as:
\[ \text{Profit} = 0.2X \]

### Step 3: Relate Selling Price to Cost Price and Profit
The selling price can also be expressed in terms of cost price and profit:
\[ X = \text{Cost Price} + \text{Profit} \]
Substituting the values we have:
\[ X = 400 + 0.2X \]

### Step 4: Rearrange the Equation
To isolate \( X \), we can rearrange the equation:
\[ X - 0.2X = 400 \]
This simplifies to:
\[ 0.8X = 400 \]

### Step 5: Solve for Selling Price
Now, divide both sides by 0.8 to find \( X \):
\[ X = \frac{400}{0.8} \]
Calculating this gives:
\[ X = 500 \]

### Conclusion
The selling price of the watch is Rs. 500.

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