A watch dealer pays 10% custom duty on a watch that costs Rs. 250 abroad. For how much should he mark it, if he desires to make a profit of 20% after giving a discount of 25% to the buyer?

Options

A. Rs. 400
B. Rs. 440
C. Rs.275
D. Rs.330

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the Cost Price Including Custom Duty
The watch dealer pays a 10% custom duty on a watch that costs Rs. 250 abroad.

- **Cost Price (CP) of the watch** = Rs. 250
- **Custom Duty** = 10% of Rs. 250 = (10/100) * 250 = Rs. 25

Now, we can find the total cost price including the custom duty:
- **Total Cost Price (CP)** = Cost Price + Custom Duty = 250 + 25 = Rs. 275

### Step 2: Calculate the Desired Selling Price for a Profit of 20%
The dealer wants to make a profit of 20% on the total cost price of Rs. 275.

- **Desired Profit** = 20% of Rs. 275 = (20/100) * 275 = Rs. 55

Now, we can find the desired selling price:
- **Selling Price (SP)** = Total Cost Price + Desired Profit = 275 + 55 = Rs. 330

### Step 3: Account for the Discount Given to the Buyer
The dealer plans to give a discount of 25% on the marked price (MP). Let’s denote the marked price as MP.

The selling price after discount can be expressed as:
- **Selling Price (SP)** = Marked Price (MP) - Discount
- **Discount** = 25% of MP = (25/100) * MP = 0.25 * MP

So, we can rewrite the equation:
- **SP** = MP - 0.25 * MP
- **SP** = 0.75 * MP

### Step 4: Set Up the Equation
From Step 2, we know that the selling price is Rs. 330. Therefore, we can set up the equation:
- 0.75 * MP = 330

### Step 5: Solve for Marked Price (MP)
To find the marked price, we can rearrange the equation:
- MP = 330 / 0.75
- MP = 330 * (100/75)
- MP = 330 * (4/3)
- MP = 440

### Conclusion
The marked price at which the dealer should sell the watch is Rs. 440.