While selling an article of marked price Rs. 5,040 at a discount of 40% if a trader gains 20% then the profit, in Rs., is:

Options

A. Rs. 2,520
B. Rs. 720
C. Rs. 642
D. Rs. 504

Answer

To solve the problem step by step, we will follow the given information and apply the relevant formulas.

### Step 1: Identify the Marked Price (MP) and Discount
- The marked price (MP) of the article is given as Rs. 5,040.
- The discount offered is 40%.

### Step 2: Calculate the Selling Price (SP)
- The selling price (SP) can be calculated using the formula:
\[ SP = MP - (Discount \% \times MP) \]
- Substitute the values:
\[ SP = 5040 - (40\% \times 5040) = 5040 - (0.40 \times 5040) = 5040 - 2016 = 3024 \]

### Step 3: Understand the Profit Percentage
- The profit percentage is given as 20%. This means that the selling price (SP) is 120% of the cost price (CP).

### Step 4: Set Up the Equation for Cost Price (CP)
- We can express this relationship as:
\[ SP = CP + Profit \]
- Since profit is 20% of CP, we can write:
\[ SP = CP + 0.20 \times CP = 1.20 \times CP \]
- Therefore, we can express CP in terms of SP:
\[ CP = \frac{SP}{1.20} \]

### Step 5: Substitute the Selling Price into the Equation
- Substitute the selling price we calculated:
\[ CP = \frac{3024}{1.20} = 2520 \]

### Step 6: Calculate the Profit in Rs.
- Now that we have the cost price (CP), we can calculate the profit:
\[ Profit = SP - CP = 3024 - 2520 = 504 \]

### Final Answer
- The profit in Rs. is **504**.

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