A shopkeeper has announced 14% rebate on marked price of an article. If the selling price of the article is X 645, then the marked price of the article will be

Options

A. X 800
B. X 810
C. X 750
D. X 775

Answer

To find the marked price of the article given a 14% rebate and a selling price of ₹645, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the terms**:
- **Marked Price (MP)**: The original price tagged on the article.
- **Selling Price (SP)**: The price at which the article is sold after the discount.
- **Rebate/Discount**: The percentage reduction on the marked price.

2. **Identify the given values**:
- Selling Price (SP) = ₹645
- Discount = 14%

3. **Set up the equation**:
- The formula for Selling Price after applying the discount is:
\[ SP = MP \times \left(1 - \frac{\text{Discount}}{100}\right) \]
- In this case, we can rewrite it as:
\[ 645 = MP \times \left(1 - \frac{14}{100}\right) \]

4. **Calculate the effective multiplier**:
- Calculate \(1 - \frac{14}{100}\):
\[ 1 - 0.14 = 0.86 \]
- So, the equation becomes:
\[ 645 = MP \times 0.86 \]

5. **Rearranging the equation to find MP**:
- To find the Marked Price (MP), we rearrange the equation:
\[ MP = \frac{645}{0.86} \]

6. **Perform the calculation**:
- Now, calculate \(MP\):
\[ MP = \frac{645}{0.86} \approx 750 \]

7. **Conclusion**:
- Therefore, the marked price of the article is ₹750.

### Final Answer:
The marked price of the article is **₹750**.

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