Marked price of a refrigerator is Rs.10800 two successive discounts each x% are given on this refrigerator. Due to further bargaining of customer discount of Rs.1808 are also allowed. Now shopkeeper charges 12.5% G.S.T on the discounted price and sold it for Rs. 4500. Find value of x ?

Options

A. `27.5%`
B. `28.33%`
C. `25%`
D. `26.66%`

Answer

To solve the problem step by step, we will first understand the situation and then derive the value of \( x \) based on the information given.

### Step-by-Step Solution:

1. **Identify the Marked Price (MP)**:
The marked price of the refrigerator is given as Rs. 10,800.

2. **Calculate the Price After Two Successive Discounts**:
Let the discount percentage be \( x\% \). After the first discount, the price becomes:
\[ \text{Price after first discount} = \text{MP} \times \left(1 - \frac{x}{100}\right) = 10800 \times \left(1 - \frac{x}{100}\right) \]
After the second discount, the price becomes:
\[ \text{Price after second discount} = \text{Price after first discount} \times \left(1 - \frac{x}{100}\right) = 10800 \times \left(1 - \frac{x}{100}\right)^2 \]

3. **Account for the Additional Bargaining Discount**:
After the two successive discounts, an additional discount of Rs. 1,808 is given. Thus, the final price before GST is:
\[ \text{Final Price before GST} = 10800 \times \left(1 - \frac{x}{100}\right)^2 - 1808 \]

4. **Calculate the Selling Price Including GST**:
The shopkeeper charges a GST of 12.5% on the discounted price. Therefore, the selling price (SP) can be expressed as:
\[ \text{Selling Price} = \text{Final Price before GST} \times \left(1 + \frac{12.5}{100}\right) = \text{Final Price before GST} \times 1.125 \]
Given that the selling price is Rs. 4,500, we can set up the equation:
\[ 4500 = \left(10800 \times \left(1 - \frac{x}{100}\right)^2 - 1808\right) \times 1.125 \]

5. **Simplify the Equation**:
Dividing both sides by 1.125 to isolate the discounted price:
\[ \frac{4500}{1.125} = 10800 \times \left(1 - \frac{x}{100}\right)^2 - 1808 \]
Calculating \( \frac{4500}{1.125} \):
\[ 4000 = 10800 \times \left(1 - \frac{x}{100}\right)^2 - 1808 \]
Rearranging gives:
\[ 4000 + 1808 = 10800 \times \left(1 - \frac{x}{100}\right)^2 \]
\[ 5808 = 10800 \times \left(1 - \frac{x}{100}\right)^2 \]

6. **Solve for \( (1 - \frac{x}{100})^2 \)**:
\[ \left(1 - \frac{x}{100}\right)^2 = \frac{5808}{10800} \]
Simplifying the fraction:
\[ \left(1 - \frac{x}{100}\right)^2 = \frac{484}{900} = \left(\frac{22}{30}\right)^2 = \left(\frac{11}{15}\right)^2 \]
Therefore:
\[ 1 - \frac{x}{100} = \frac{11}{15} \]

7. **Calculate \( x \)**:
\[ \frac{x}{100} = 1 - \frac{11}{15} = \frac{4}{15} \]
Thus:
\[ x = \frac{4}{15} \times 100 = \frac{400}{15} = 26.67 \]

### Conclusion:
The value of \( x \) is approximately \( 26.67\% \).