A trader marked a watch `40%` above the cost price and then gave a discount of `10%` . He made a net profit of Rs. 468 after paying a tax of `10%` on the gross profit. What is the cost price of the watch?

Options

A. Rs .1200
B. Rs.1800
C. Rs.2000
D. Rs.2340

Answer

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

### Step 1: Define Variables
Let:
- \( CP \) = Cost Price
- \( MP \) = Marked Price
- \( SP \) = Selling Price

### Step 2: Calculate Marked Price
The watch is marked 40% above the cost price. Therefore, we can express the marked price as:
\[ MP = CP + 0.4 \times CP = 1.4 \times CP \]

### Step 3: Calculate Selling Price
A discount of 10% is given on the marked price. Thus, the selling price can be calculated as:
\[ SP = MP - 0.1 \times MP = 0.9 \times MP \]
Substituting the expression for \( MP \):
\[ SP = 0.9 \times (1.4 \times CP) = 1.26 \times CP \]

### Step 4: Calculate Gross Profit
The gross profit is given by:
\[ \text{Gross Profit} = SP - CP = (1.26 \times CP) - CP = 0.26 \times CP \]

### Step 5: Calculate Net Profit After Tax
The trader pays a tax of 10% on the gross profit. Therefore, the amount he keeps after tax is:
\[ \text{Net Profit} = \text{Gross Profit} - \text{Tax} \]
The tax on the gross profit is:
\[ \text{Tax} = 0.1 \times \text{Gross Profit} = 0.1 \times (0.26 \times CP) = 0.026 \times CP \]
Thus, the net profit after tax is:
\[ \text{Net Profit} = 0.26 \times CP - 0.026 \times CP = 0.234 \times CP \]

### Step 6: Set Up the Equation
We know from the problem statement that the net profit is Rs. 468. Therefore, we can set up the equation:
\[ 0.234 \times CP = 468 \]

### Step 7: Solve for Cost Price
To find \( CP \), we divide both sides by 0.234:
\[ CP = \frac{468}{0.234} \approx 2000 \]

### Conclusion
The cost price of the watch is Rs. 2000.

---