By selling a watch for Rs. 800, a dealer gained `1/4` of its cost price. Find the cost price of the watch.

Answer

To find the cost price of the watch, we will follow these steps:

### Step 1: Understand the given information
The selling price (SP) of the watch is Rs. 800, and the dealer gains \( \frac{1}{4} \) of the cost price (CP).

### Step 2: Set up the equations
Let the cost price of the watch be \( x \) rupees. According to the problem, the profit is \( \frac{1}{4} \) of the cost price. Therefore, we can express the profit as:
\[ \text{Profit} = \frac{1}{4} \times x = \frac{x}{4} \]

### Step 3: Relate SP, CP, and Profit
The selling price can be expressed in terms of cost price and profit:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Substituting the values we have:
\[ 800 = x + \frac{x}{4} \]

### Step 4: Solve for \( x \)
To solve the equation, first, we need to combine the terms on the right side. We can rewrite \( x \) as \( \frac{4x}{4} \) to have a common denominator:
\[ 800 = \frac{4x}{4} + \frac{x}{4} \]
This simplifies to:
\[ 800 = \frac{4x + x}{4} = \frac{5x}{4} \]

Now, to eliminate the fraction, multiply both sides by 4:
\[ 3200 = 5x \]

Now, divide both sides by 5 to find \( x \):
\[ x = \frac{3200}{5} = 640 \]

### Step 5: Conclusion
The cost price of the watch is Rs. 640.

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