A dealer allows his customers a discount of 25% and still gains 25%. If an article costs Rs 1,440 to the dealer, find :
its marked price

Answer

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

### Step 1: Understand the given information
- Cost Price (CP) of the article = Rs 1,440
- Discount allowed = 25%
- Profit gained = 25%

### Step 2: Calculate the Selling Price (SP)
Since the dealer gains a profit of 25%, we can calculate the Selling Price (SP) using the formula:
\[ SP = CP + \text{Profit} \]
Profit is calculated as:
\[ \text{Profit} = \frac{25}{100} \times CP = \frac{25}{100} \times 1440 = 360 \]
Now, substituting this back into the SP formula:
\[ SP = 1440 + 360 = 1800 \]

### Step 3: Relate Selling Price to Marked Price
The Selling Price (SP) is also related to the Marked Price (MP) by the discount given. The formula for SP when a discount is applied is:
\[ SP = MP - \text{Discount} \]
Since the discount is 25% of the Marked Price, we can express this as:
\[ SP = MP - 0.25 \times MP = MP \times (1 - 0.25) = MP \times 0.75 \]

### Step 4: Set up the equation
Now we can set up the equation using the Selling Price calculated in Step 2:
\[ 1800 = MP \times 0.75 \]

### Step 5: Solve for Marked Price (MP)
To find the Marked Price (MP), we can rearrange the equation:
\[ MP = \frac{1800}{0.75} \]
Calculating this gives:
\[ MP = 2400 \]

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

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