Goods and Services Tax (GST) notes: ICSE Class 10 Mathematics

1. What GST is

The Goods and Services Tax (GST) is a single tax on the supply of goods and services in India, in force since 1 July 2017. It replaced many earlier indirect taxes (central excise, VAT, service tax and others).

It is charged at every sale in a supply chain: manufacturer → wholesaler → retailer → consumer.
It applies to services as well as goods (repairs, catering, rent, software).
The buyer pays it, the seller collects it and passes it to the government.
Rates are fixed for each item by the GST Council and are revised from time to time. In every problem the rate is given; this chapter uses 5%, 12%, 18% and 28%.

GST is charged at every sale in the chain, not only at the shop counter.

Formulas

GST at rate r%
$\text{GST} = \dfrac{r}{100} \times \text{taxable value}$

Key terms

GST: Goods and Services Tax: one tax on the supply of goods and services across India.
Taxable value: The price on which GST is charged: the selling price after any discount, before tax.
GST Council: The body of the Union and state finance ministers that fixes and revises GST rates.

2. CGST, SGST and IGST

Where the seller and the buyer are decides the heads of tax:

Intra-state sale (same state): the bill shows CGST (central) and SGST (state), each at half the GST rate.
Inter-state sale (different states): the bill shows IGST (integrated) at the full rate. The Centre collects it and shares it with the state where the goods are used.

The rate and the total tax are the same in both cases; only the heads differ. (In a union territory without its own legislature, UTGST takes the place of SGST.)

Example: a pump priced ₹15,500 at 18%: Coimbatore to Palakkad, IGST ₹2,790; Coimbatore to Tiruppur, CGST ₹1,395 + SGST ₹1,395.

Where the buyer is decides the heads of tax, not the rate.
Sale	Example	Tax on the bill	Collected by
Intra-state (same state)	Nagpur to Pune, both in Maharashtra	CGST + SGST, half the rate each	Centre (CGST) and the state (SGST)
Inter-state (different states)	Coimbatore (Tamil Nadu) to Palakkad (Kerala)	IGST at the full rate	Centre, which shares it with the state where the goods are used

Within a state the rate is halved; across states it is charged whole as IGST.
GST rate	CGST	SGST	IGST (inter-state)
5%	2.5%	2.5%	5%
12%	6%	6%	12%
18%	9%	9%	18%
28%	14%	14%	28%

Formulas

Intra-state
$\text{CGST} = \text{SGST} = \dfrac{1}{2}\,\text{GST}$
Inter-state
$\text{IGST} = \text{GST}$

Key terms

CGST: Central GST on an intra-state sale, at half the GST rate.
SGST: State GST on an intra-state sale, at half the GST rate.
IGST: Integrated GST on an inter-state sale, at the full rate.

3. The tax invoice

A registered seller issues a tax invoice showing the taxable value of each item, the rate and amount of CGST and SGST (or IGST), and the invoice value.

With items at different rates, tax each line at its own rate, then add:

School bag ₹1,200 at 12%: GST ₹144
Calculator ₹850 at 18%: GST ₹153
Notebooks ₹400 at 5%: GST ₹20

Total GST ₹317; CGST = SGST = ₹158.50; invoice value ₹2,767.

Invoice value $= 2450 + 317 = 2767$ rupees.
Item	Price (₹)	Rate	GST (₹)	CGST (₹)	SGST (₹)
School bag	1,200	12%	144	72	72
Scientific calculator	850	18%	153	76.50	76.50
Pack of notebooks	400	5%	20	10	10
Total	2,450		317	158.50	158.50

Formulas

Bill
$\text{invoice value} = \text{taxable value} + \text{CGST} + \text{SGST} \ (\text{or} + \text{IGST})$

Key terms

Tax invoice: The bill a registered seller issues, showing taxable value, each tax and the total.
Invoice value: Taxable value plus all the taxes: the amount the buyer pays.

4. Discount and GST: what the consumer pays

GST is charged on the selling price after discount, never on the list price.

Discount = d% of the list price; selling price = list price − discount.
GST = r% of the selling price.
Amount paid = selling price + GST = list price × (1 − d/100) × (1 + r/100).

Example: list price ₹24,000, 15% off, GST 18%: selling price ₹20,400, GST ₹3,672, amount ₹24,072. Note that 15% off and 18% on multiply to 1.003, not 1.03.

Discount first, then tax on what is left.

GST on the list price (wrong)
15% off, then 18% GST (right)

Taxing the list price would overcharge by more than four thousand rupees here.

Formulas

List price L, discount d%, GST r%
$\text{amount} = L\left(1 - \dfrac{d}{100}\right)\left(1 + \dfrac{r}{100}\right)$

Key terms

List (marked) price: The price printed or quoted before any discount.
Selling price: The list price minus the discount; it is the taxable value.

5. Input tax credit and GST with profit or loss

A dealer pays GST on purchases (input tax) and collects GST on sales (output tax). Through input tax credit it pays only the difference:

\text{net GST} = \text{output tax} - \text{input tax}.

Within a state, CGST payable = SGST payable = half the net GST.
At one rate, net GST = r% of (selling price − purchase price): tax on the value added.
Profit and loss are worked out on prices before tax; the tax is passed on, not earned.
At a loss, output tax < input tax: nothing is payable and the difference stays as credit.

Example: cost ₹5,000, marked 20% up, 10% off, GST 12%: selling price ₹5,400, net GST ₹48 (CGST ₹24 + SGST ₹24), customer pays ₹6,048, profit 8%.

Input tax credit: pay only the difference.

Net GST $= 648 - 600 = 48$ rupees.

Formulas

Tax payable by a dealer
$\text{net GST} = \text{output tax} - \text{input tax}$
One rate throughout
$\text{net GST} = \dfrac{r}{100}(\text{SP} - \text{CP})$

Key terms

Input tax: GST a dealer pays when it buys goods or services for its business.
Output tax: GST a dealer charges and collects when it sells.
Input tax credit (ITC): Setting off input tax against output tax, so that only the difference is paid.

6. The supply chain: tax at each stage

Make a table: stage, selling price, output tax, input tax, net GST (and CGST, SGST).

The first seller has no input tax and pays the full GST on its price.
Each later dealer pays output tax minus the previous stage's output tax.
Adding the payments, the intermediate taxes cancel: total GST to the government = GST on the final sale, which the consumer bears.

Example (18%, all in Gujarat): sales at ₹3,000, ₹3,600, ₹4,200; payments ₹540, ₹108, ₹108; total ₹756 = 18% of ₹4,200. Without input tax credit the taxes would total ₹1,944 (tax on tax).

Inter-state link: the seller charges IGST and sets off its input CGST and SGST: IGST payable = output IGST − input CGST − input SGST. Example: ₹5,520 − ₹4,800 = ₹720.

Each row: output tax minus input tax, then halve.
Stage	Sells for (₹)	Output tax (₹)	Input tax (₹)	Net GST (₹)	CGST (₹)	SGST (₹)
Manufacturer (Surat)	3,000	540	0	540	270	270
Wholesaler (Vadodara)	3,600	648	540	108	54	54
Retailer (Rajkot)	4,200	756	648	108	54	54

Manufacturer pays
Wholesaler pays
Retailer pays
Consumer's tax

The first three bars add up to the fourth.

Input CGST and SGST can both be used against output IGST.
Link	Tax charged	Input tax set off	Paid to the government
Ludhiana maker to Ludhiana distributor (intra-state)	CGST 2,400 + SGST 2,400	none	4,800
Ludhiana distributor to Jaipur retailer (inter-state)	IGST 5,520	CGST + SGST 4,800	IGST 720

Formulas

Whole chain, one rate
$\text{total GST} = \dfrac{r}{100} \times \text{final selling price}$

Key terms

Supply chain: The sequence of sales from manufacturer to wholesaler to retailer to consumer.
Cascading: Tax charged on a price that already includes tax; input tax credit prevents it.

7. Reverse problems

Undo the steps in reverse order: the tax was added last, so remove it first.

Price before GST: price = amount × 100/(100 + r). Example: ₹11,092 at 18% → ₹9,400.
Rate of GST: r = (amount − price)/price × 100. Example: ₹2,300 → ₹2,576 gives 12%.
List price: list = selling price ÷ (1 − d/100). Example: ₹4,956 after 16% off and 18% GST → selling price ₹4,200 → list ₹5,000.
Rate of discount: d = (list − selling price)/list × 100.
From a dealer's payment at one rate: its margin = payment × 100/r.

Never take r% off the amount: 82% of ₹1,180 is ₹967.60, but the price is ₹1,000.

Work backwards: undo the tax first, then the discount.
Find	Rule
Price before GST	$\text{price} = \text{amount} \times \dfrac{100}{100 + r}$
Rate of GST	$r = \dfrac{\text{amount} - \text{price}}{\text{price}} \times 100$
Price after discount	$\text{amount} \div \left(1 + \dfrac{r}{100}\right)$
List price	$\text{selling price} \div \left(1 - \dfrac{d}{100}\right)$
Rate of discount	$d = \dfrac{\text{list} - \text{selling price}}{\text{list}} \times 100$

amount = 1.18 × price

Reading back from the amount to the price means dividing by 1.18.

Formulas

Price before GST
$\text{price} = \text{amount} \times \dfrac{100}{100 + r}$
Rate of GST
$r = \dfrac{\text{amount} - \text{price}}{\text{price}} \times 100$

Key terms

Reverse (inverse) problem: A problem that gives the final amount and asks for an earlier quantity: price, rate, list price or discount.

Exam tips

How marks are awarded

GST on a bill (2–3 marks): GST on each item (1), CGST and SGST or IGST correctly chosen and split (1), invoice value (1).
Discount and GST (3 marks): selling price after discount (1), GST on the selling price (1), amount paid (1).
Supply chain (4 marks in Section A, or a 3 + 3 + 4 structured question): selling price at each stage (1), output and input tax (1), net GST of each dealer (1), CGST/SGST split or the total equal to the consumer's tax (1).
Reverse problems (3–4 marks): equation such as $1.18x = \text{amount}$ (1), price (1), then rate, list price or discount (1–2).

Common mistakes

Charging GST on the list price instead of the price after discount.
Using IGST for a sale within a state, or CGST and SGST for a sale between states.
Writing CGST at the full rate instead of half.
Forgetting that the first seller in a chain has no input tax.
Adding the output taxes of all stages to get the government's total.
Working out profit on prices that include GST.
Taking r% off the amount paid to remove the tax (divide by 1 + r/100 instead).
Rounding paise: ₹158.50 is exact, not ₹159.

1. What GST is

Formulas

Key terms

2. CGST, SGST and IGST

Formulas

Key terms

3. The tax invoice

Formulas

Key terms

4. Discount and GST: what the consumer pays

Formulas

Key terms

5. Input tax credit and GST with profit or loss

Formulas

Key terms

6. The supply chain: tax at each stage

Formulas

Key terms

7. Reverse problems

Formulas

Key terms

Exam tips

Cookies