Ever wondered why every receipt you get ends with a mysterious "GST" amount? It’s not magic – it’s just a tax that helps run the country.
💡 In Simple Words: GST (Goods and Services Tax) is a single tax added to the price of most things you buy. It can be shown as part of the price (inclusive) or added on top (exclusive). Knowing how to switch between the two makes solving maths problems a breeze.
What is GST?
GST stands for Goods and Services Tax. Think of it as a common tax that the government charges on almost everything you buy or sell. Before GST, each state had its own tax, which made calculations messy. GST simplifies everything into one rate.
Why does GST matter in maths?
In commercial maths, you often need to find the final price after tax or work backwards to discover the original price before tax. It’s like figuring out how much water is in a pipe when you know the flow rate and the pressure.
How to calculate GST
There are two common ways GST appears:
- Exclusive GST: The tax is added to the listed price. Example: A shirt costs ₹500, GST is 5%. Total = ₹500 + (5% of ₹500).
- Inclusive GST: The listed price already includes tax. Example: A toy is sold for ₹525, which already contains 5% GST. You need to peel the tax away to know the base price.
Below is a quick flow of the steps you’ll use most often.
Example 1: Exclusive GST
Problem: A notebook is priced at ₹120. GST is 12%. Find the total amount you pay.
Solution:
- Find GST amount: 12% of ₹120 = (12/100) × 120 = ₹14.40.
- Add to the original price: 120 + 14.40 = ₹134.40.
So you pay ₹134.40.
Example 2: Inclusive GST
Problem: A backpack is sold for ₹1,260, and the price includes 5% GST. What is the price before GST and how much GST was charged?
Solution:
- Let the original price be P. Since the price includes 5% GST, the total equals P × (1 + 5/100) = P × 1.05.
- Set up the equation: P × 1.05 = 1,260 → P = 1,260 ÷ 1.05 = ₹1,200.
- GST amount = Total – Original = 1,260 – 1,200 = ₹60.
Thus, the backpack’s base price is ₹1,200 and GST is ₹60.
Example 3: Finding GST rate from given prices
Problem: A pair of shoes costs ₹2,200 after GST. If the original price was ₹2,000, what GST rate was applied?
Solution:
- GST amount = 2,200 – 2,000 = ₹200.
- Rate = (GST ÷ Original) × 100 = (200 ÷ 2,000) × 100 = 10%.
The GST rate is 10%.
Quick Comparison: Inclusive vs. Exclusive GST
| Aspect | Exclusive GST | Inclusive GST |
|---|---|---|
| How price is shown | Base price + GST added later | GST already built into the listed price |
| Common use | Invoices, quotations | Retail displays, online shopping |
| Key formula | Total = Price × (1 + Rate) | Original = Total ÷ (1 + Rate) |
Tips for ICSE Exams
- Always write down whether the given price is inclusive or exclusive.
- Convert percentages to decimals before multiplying (12% → 0.12).
- When working backwards, remember to divide by (1 + rate) instead of subtracting.
- Check your units – GST is always in rupees, not in percent.
📝 Likely Exam Questions
- Question: A mobile phone is priced at ₹15,000 before GST. If GST is 18%, calculate the selling price.
Answer: GST = 0.18 × 15,000 = ₹2,700. Selling price = 15,000 + 2,700 = ₹17,700. - Question: A television set is sold for ₹42,000 inclusive of 12% GST. Find the base price and the GST amount.
Answer: Base price = 42,000 ÷ 1.12 = ₹37,500. GST = 42,000 – 37,500 = ₹4,500. - Question: A shopkeeper bought goods worth ₹8,500 and sold them for ₹10,000 after adding 5% GST. What was his profit before tax?
Answer: Selling price before GST = 10,000 ÷ 1.05 = ₹9,523.81. Profit before tax = 9,523.81 – 8,500 = ₹1,023.81. - Question: If the GST rate is 28% and the total price of a laptop is ₹71,600, what is the laptop’s original price?
Answer: Original price = 71,600 ÷ 1.28 = ₹55,937.50.