Sure, let's break down the problem step-by-step to find the price of the TV before the GST was added.
1. Identify the given information:
- The total price including GST: Rs. 54,000
- The GST rate: 12%
2. Understand the relationship between the total price and the price before GST:
- When GST is added to the original price, the total price becomes the original price plus the GST.
- In other words, [tex]\( \text{Total Price} = \text{Price Before GST} + \text{GST Amount} \)[/tex]
3. Express the GST amount in terms of the original price:
- The GST amount is a percentage of the price before GST. In this case, it is 12% of the price before GST.
4. Mathematical Formulation:
- If [tex]\( P \)[/tex] is the price before GST, then the GST amount is [tex]\( 0.12P \)[/tex].
- Therefore, the total price including GST can be written as: [tex]\( \text{Total Price} = P + 0.12P \)[/tex]
- Simplifying this, we get: [tex]\( \text{Total Price} = 1.12P \)[/tex]
5. Rearrange to solve for [tex]\( P \)[/tex]:
- Given that the total price is Rs. 54,000, we set up the equation: [tex]\( 54000 = 1.12P \)[/tex]
- Now, solve for [tex]\( P \)[/tex] by dividing both sides of the equation by 1.12:
[tex]\[ P = \frac{54000}{1.12} \][/tex]
6. Calculate the price before GST:
- Performing the division will give us the price before GST:
[tex]\[ P \approx 48214.29 \][/tex]
So, the price of the TV before the GST was added is approximately Rs. 48,214.29.
