A dealer sells an article by allowing a `20%` discount on its marked price and still gains `12%`. If the cost price of the article is 750, then its marked price (in) is:

Options

A. 1050
B. 1025
C. 1150
D. 1125

Answer

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

### Step 1: Identify the Cost Price and Gain Percentage
The cost price (CP) of the article is given as ₹750, and the gain percentage is 12%.

### Step 2: Calculate the Selling Price
To find the selling price (SP), we can use the formula:
\[ SP = CP + \text{Gain} \]
The gain can be calculated as:
\[ \text{Gain} = \left(\frac{\text{Gain Percentage}}{100}\right) \times CP = \left(\frac{12}{100}\right) \times 750 = 90 \]
Now, substituting the gain back into the SP formula:
\[ SP = 750 + 90 = 840 \]

### Step 3: Relate Selling Price to Marked Price
The dealer sells the article at a 20% discount on the marked price (MP). This means:
\[ SP = MP - \left(\frac{20}{100} \times MP\right) \]
This can be simplified to:
\[ SP = MP \times \left(1 - 0.20\right) = MP \times 0.80 \]

### Step 4: Substitute the Selling Price into the Equation
Now we can substitute the selling price we found into the equation:
\[ 840 = MP \times 0.80 \]

### Step 5: Solve for Marked Price
To find the marked price (MP), we can rearrange the equation:
\[ MP = \frac{840}{0.80} \]
Calculating this gives:
\[ MP = 1050 \]

### Conclusion
The marked price of the article is ₹1050.

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