A retailer gives 40% discount on a certain article, to his customer. In this transaction he earns a profit of 25% on that article. If the article costs Rs. 4,320 to the retailer, what is its marked price (in Rs.)?

Options

A. 8000
B. 2592
C. 9000
D. 6000

Answer

To find the marked price of the article, we can follow these steps:

### Step 1: Understand the given information
- Cost Price (CP) of the article = Rs. 4,320
- Discount offered = 40%
- Profit earned = 25%

### Step 2: Calculate the Selling Price (SP)
Since the retailer earns a profit of 25%, we can calculate the Selling Price using the formula:
\[ SP = CP + (Profit \% \times CP) \]
Substituting the values:
\[ SP = 4320 + (25\% \times 4320) \]
\[ SP = 4320 + \left(\frac{25}{100} \times 4320\right) \]
\[ SP = 4320 + 1080 = 5400 \]

### Step 3: Relate Selling Price to Marked Price
The Selling Price is also related to the Marked Price (MP) through the discount. If the Marked Price is MP, then:
\[ SP = MP - (Discount \% \times MP) \]
Since a 40% discount is given, we can express this as:
\[ SP = MP - (40\% \times MP) = MP \times (1 - 0.40) = MP \times 0.60 \]

### Step 4: Set up the equation
Now we can set the Selling Price equal to the expression involving the Marked Price:
\[ 5400 = MP \times 0.60 \]

### Step 5: Solve for Marked Price
To find the Marked Price, rearrange the equation:
\[ MP = \frac{5400}{0.60} \]
Calculating this gives:
\[ MP = 5400 \div 0.60 = 9000 \]

### Conclusion
The Marked Price of the article is Rs. 9,000.

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