A dealer allows his cstomers a discount of 25% and still gains 25%. If an article costs 1,440 to the dealer, then its marked price is

Options

A. Rs 2,560
B. Rs 1,500
C. Rs 1,850
D. Rs 2400

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 = ₹1,440
- Discount offered = 25%
- Profit gained = 25%

### Step 2: Calculate the Selling Price (SP)
Since the dealer gains a profit of 25% on the Cost Price, we can calculate the Selling Price using the formula:

\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]

Profit can be calculated as:

\[ \text{Profit} = \frac{25}{100} \times \text{CP} = \frac{25}{100} \times 1440 = 360 \]

Now, substituting the profit back into the SP formula:

\[ \text{SP} = 1440 + 360 = 1800 \]

### Step 3: Relate Selling Price to Marked Price
The Selling Price is also related to the Marked Price (MP) and the discount given. The relationship can be expressed as:

\[ \text{SP} = \text{MP} - \text{Discount} \]

Given that the discount is 25% of the Marked Price, we can express this as:

\[ \text{Discount} = \frac{25}{100} \times \text{MP} = 0.25 \times \text{MP} \]

Substituting this into the SP equation gives:

\[ \text{SP} = \text{MP} - 0.25 \times \text{MP} = 0.75 \times \text{MP} \]

### Step 4: Solve for the Marked Price
Now, we can set the Selling Price equal to 0.75 times the Marked Price:

\[ 1800 = 0.75 \times \text{MP} \]

To find the Marked Price (MP), we can rearrange the equation:

\[ \text{MP} = \frac{1800}{0.75} \]

Calculating this gives:

\[ \text{MP} = 2400 \]

### Final Answer
The marked price of the article is ₹2,400.

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