The cost price of an article is X 800. After allowing a discount of 10%, a gain of 12.5% was made. Then, the marked price of the article is

Options

A. ?1000
B. ?1100
C. ?1200
D. ?1300

Answer

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

### Step 1: Understand the given information
- Cost Price (CP) = ₹800
- Discount = 10%
- Gain = 12.5%

### Step 2: Set up the equation for Selling Price (SP)
The Selling Price after applying the discount can be calculated using the formula:
\[ SP = MP \times \left(1 - \frac{\text{Discount}}{100}\right) \]
Where MP is the Marked Price.

### Step 3: Express Selling Price in terms of Marked Price
Substituting the discount into the formula:
\[ SP = MP \times \left(1 - \frac{10}{100}\right) = MP \times \frac{90}{100} = 0.9 \times MP \]

### Step 4: Relate Selling Price to Gain
The Selling Price can also be expressed in terms of the Cost Price and Gain Percentage:
\[ SP = CP \times \left(1 + \frac{\text{Gain}}{100}\right) \]
Substituting the values:
\[ SP = 800 \times \left(1 + \frac{12.5}{100}\right) = 800 \times 1.125 = 900 \]

### Step 5: Set the two expressions for Selling Price equal to each other
Now we have two expressions for Selling Price:
\[ 0.9 \times MP = 900 \]

### Step 6: Solve for Marked Price (MP)
To find MP, divide both sides by 0.9:
\[ MP = \frac{900}{0.9} = 1000 \]

### Conclusion
Thus, the Marked Price of the article is ₹1000.

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