I purchased a hair-dryer for `Rs. 5,400` including `8%` VAT. Find the price before VAT was added.

Options

A. `Rs. 5400`
B. `Rs. 4000`
C. `Rs. 4500`
D. `Rs. 6500`

Explanation

To find the price of the hair-dryer before VAT was added, we can follow these steps:

### Step 1: Understand the given information
We know that the total price of the hair-dryer, including VAT, is Rs. 5,400 and the VAT rate is 8%.

### Step 2: Set up the equation
Let the price before VAT be \( X \). The VAT amount can be calculated as 8% of \( X \), which is \( \frac{8}{100} \times X = \frac{2}{25}X \).

The total price including VAT can be expressed as:
\[ \text{Total Price} = \text{Price before VAT} + \text{VAT} \]
This translates to:
\[ 5400 = X + \frac{2}{25}X \]

### Step 3: Combine like terms
To combine \( X \) and \( \frac{2}{25}X \), we can express \( X \) as \( \frac{25}{25}X \):
\[ 5400 = \frac{25}{25}X + \frac{2}{25}X = \frac{27}{25}X \]

### Step 4: Solve for \( X \)
Now, we can solve for \( X \) by multiplying both sides of the equation by \( \frac{25}{27} \):
\[ X = 5400 \times \frac{25}{27} \]

### Step 5: Calculate the value
Now, we can calculate \( 5400 \times \frac{25}{27} \):
1. First, divide \( 5400 \) by \( 27 \):
\[ 5400 \div 27 = 200 \]
2. Now multiply by \( 25 \):
\[ 200 \times 25 = 5000 \]

### Conclusion
Thus, the price before VAT was added is \( Rs. 5000 \).