A store offers a variety of discounts that range between 20% and 25% inclusive. If a book is dicounted to a price of Rs. 270, then its greatest possible original price was

Options

A. Rs 345.5
B. Rs. 324
C. Rs. 360
D. Rs. 337.5

Answer

To find the greatest possible original price of the book after a discount of 25%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Discount**: The store offers discounts between 20% and 25%. To find the greatest possible original price, we will use the maximum discount of 25%.

2. **Set Up the Equation**: Let the original price of the book be \( X \). If the discount is 25%, then the price after discount can be expressed as:
\[ \text{Price after discount} = X - 0.25X = 0.75X \]
We know that the price after discount is Rs. 270. Therefore, we can set up the equation:
\[ 0.75X = 270 \]

3. **Solve for \( X \)**: To find \( X \), we can rearrange the equation:
\[ X = \frac{270}{0.75} \]

4. **Calculate \( X \)**: To simplify \( \frac{270}{0.75} \), we can multiply both the numerator and the denominator by 100 to eliminate the decimal:
\[ X = \frac{270 \times 100}{75} \]

5. **Simplify the Fraction**: Now we can simplify \( \frac{27000}{75} \):
- Divide both the numerator and the denominator by 15:
\[ X = \frac{27000 \div 15}{75 \div 15} = \frac{1800}{5} = 360 \]

6. **Conclusion**: The greatest possible original price of the book is Rs. 360.