Goods and Services Tax (GST) | ICSE Class 10 Maths Notes

This note covers Goods and Services Tax, prices before and after tax, Central and State GST, discounts, list price, cost price, profit and loss, percentage calculations, and inverse problems involving the amount paid by a consumer.

What is GST, and which prices must you distinguish?

Definition: Goods and Services Tax (GST) is a tax levied on the supply of goods or services or both. Goods are articles supplied, while services are activities supplied for payment.

A consumer is the buyer who uses the goods or services. In a calculation involving tax added to a price, distinguish the price before tax, the tax amount, and the final amount paid. These are separate quantities even when the question calls more than one of them a price.

How do the price labels differ?

The list price, also called the marked price, is the stated price before a discount. A discount is a reduction from that price. The selling price after this reduction is the price to examine when calculating GST on the discounted sale.

The basic price means the price before GST in the calculation being considered. The taxable value is the amount on which GST is calculated. In the simple discounted-sale problems here, it is the selling price after the stated discount and before GST.

The cost price is the cost of an article to its seller. The selling price is the price at which the seller sells it.

Profit is selling price less cost price when selling price is greater. Loss is cost price less selling price when cost price is greater. For these comparisons below, use prices before GST and follow the specified cost basis.

A tax-inclusive price includes GST; a tax-exclusive price excludes it. Read “including GST” before choosing a formula: it changes a direct percentage calculation into a calculation that works backwards from the total.

How do percentages produce the GST formulas?

A percentage is a quantity expressed per hundred; the symbol % means per cent. The percentage base is the quantity treated as the whole, or 100%. GST percentage is applied to the taxable value, so identify that value before multiplying.

Let B denote the basic taxable price, r the numerical GST rate expressed as a percentage, T the GST amount, and A the amount including GST. All money amounts must use the same currency. The symbol ₹ denotes Indian rupees.

In the formulas, = means equals, + means addition, − means subtraction, × means multiplication, and / means division. Adjacent letters or brackets also indicate multiplication. A numerator is the quantity above a fraction bar; a denominator is the quantity below it.

Result: The direct tax calculation

T = Br/100. Here multiplication is indicated by adjacent letters. This formula says that the tax is r hundredths of the taxable price. A rate supplied as a percentage must therefore be divided by 100 when used as a multiplier, a factor used to multiply a quantity.

A = B + T = B(100 + r)/100. The brackets group the sum before multiplication. The final amount contains the whole basic price as well as the tax, so adding tax increases a positive price when the given rate is positive.

Result: Recovering the price before GST

B = 100A/(100 + r). This follows by multiplying the equation for A by 100, then dividing by 100 + r. An inverse calculation recovers an earlier quantity from a later result by undoing the operations used to obtain it.

The corresponding tax formula is T = Ar/(100 + r). Subtracting B from A gives the same answer. Notice that the denominator is 100 + r because the known total includes the original hundred parts and the additional tax parts.

Note: Finding r% of A does not recover GST already included in A. That would calculate a fresh percentage on the larger, tax-inclusive amount instead of on B.

Use the formula with the quantity actually given. A price before GST leads naturally to multiplication; an amount including GST leads naturally to division by the tax multiplier, (100 + r)/100. Writing the labels beside the data often prevents choosing the wrong direction.

How are CGST and SGST calculated on the same price?

Central Goods and Services Tax (CGST) and State Goods and Services Tax (SGST) are the central and state components used in the same-state transactions considered here. A same-state transaction is one described as taking place within the same state.

When both component rates are given, apply each to the same taxable value. The CGST amount is not added to the price before calculating SGST. Neither component is a percentage of the other component.

Let c and s denote the numerical CGST and SGST percentage rates. Then CGST amount = Bc/100, SGST amount = Bs/100, and total GST rate r = c + s. If the stated component rates are equal, each is half their total.

How do you show the consumer's total?

1. Identify the price before GST, after any discount allowed before tax.
2. Multiply that price by the stated CGST rate and divide by 100.
3. Calculate SGST separately on the same price using its stated rate.
4. Add the basic price and both tax amounts to find the amount payable.

Worked example 1. A computer printer has a price before GST of ₹10,000. For this same-state transaction, CGST is 5% and SGST is 5%. Find both tax amounts and the total payable.

Answer: CGST = ₹10,000 × 5/100 = ₹500. SGST = ₹10,000 × 5/100 = ₹500. Total GST = ₹1,000. The amount payable is ₹10,000 + ₹500 + ₹500 = ₹11,000.

The two given rates together represent 10% GST in this example. Treating 5% as the complete GST rate would omit a component. Treating each component as 10% would count twice the tax specified by the question.

The separation also gives a useful arithmetic check: add the component amounts first, then calculate the combined percentage directly on the basic price. The results must agree because both components use the same base.

How do you calculate bills for goods and services?

A bill records the charges and the amount payable. For a straightforward GST bill, organise the calculation into a price before tax, the tax components, and the final total. Keeping these columns separate makes both the arithmetic and the meaning of the answer clearer.

Goods and services use the same percentage method when the price and tax rates are supplied. A transport charge, for example, is the basic charge for a service. The tax is calculated on that charge before the components are added to obtain the amount payable.

How does the method apply to a service charge?

Worked example 2. Railway transport charges before tax are ₹8,000. The stated CGST and SGST rates are 5% each. Find the tax amounts and the total charge including GST.

Answer: CGST = ₹8,000 × 5/100 = ₹400. SGST = ₹8,000 × 5/100 = ₹400. The total tax is ₹800, and the total charge is ₹8,000 + ₹400 + ₹400 = ₹8,800.

The following calculations use the rates stated for these transactions. They illustrate how the components are added; they are not a schedule of rates to apply to purchases where different rates are supplied.

Read each row independently. The basic value plus the two tax components must equal the total in that row. A component check means checking these separate parts against their sum before accepting the final amount.

If a question contains several items with different stated rates, calculate the tax for each taxable amount at its own rate, then add the results. Do not apply one item's percentage to the whole bill unless that percentage applies to every amount included.

How does a discount change the price before GST?

A discount reduces the marked price. It is generally given to attract customers or promote sales. The discount percentage uses the marked price as its base, even though the amount eventually paid can be different because of both discount and GST.

Let M denote the marked or list price, d the numerical discount percentage, and D the discount amount. Then D = Md/100. When the stated discount is allowed before GST, the resulting taxable price is B = M − D.

Result: Discount followed by GST

B = M(100 − d)/100. Applying GST after this discount gives A = M(100 − d)(100 + r)/10000. The denominator comes from multiplying the two percentage denominators, 100 × 100.

Worked example 3. A frock has a list price of ₹220 and a discount of 20%. Find the discount and the sale price before any tax calculation.

Answer: Discount = ₹220 × 20/100 = ₹44. Sale price = ₹220 − ₹44 = ₹176. Equivalently, the buyer pays 80% of the list price, so the sale price is ₹220 × 80/100 = ₹176.

No GST rate is supplied in this example, so the ₹176 answer is the discounted sale price. It does not establish a GST-inclusive total. A later tax calculation would require a stated rate and would use this discounted price when tax follows discount.

Why are the two percentages kept separate?

The discount acts on M, whereas the GST acts on B. Subtracting the discount rate from the GST rate and applying the difference to M ignores the change of base. The correct combined calculation is a product of the two multipliers.

A multiplier is the factor by which a quantity is multiplied to obtain a new quantity. Here the discount multiplier is (100 − d)/100, and the tax multiplier is (100 + r)/100. Showing these separately explains both the operation and its order.

How can you recover a discount or a list price?

Discount questions can work backwards in two different ways. If marked price and sale price are both known, subtract to find the discount and then compare it with the marked price. If the sale price and discount percentage are known, recover the whole marked price by division.

How do you find the discount percentage?

d = 100(M − B)/M, when B is the sale price after discount and before tax. The numerator contains the reduction; the denominator contains the original marked price. Dividing by the reduced price would answer a different percentage question.

Worked example 4. An article marked at ₹840 is sold for ₹714 before any tax calculation. Find the discount amount and discount percentage.

Answer: Discount = ₹840 − ₹714 = ₹126. Discount percentage = 126/840 × 100% = 15%. The marked price, ₹840, is the percentage base because the reduction is measured against that original price.

How do you recover the marked price?

M = 100B/(100 − d), provided the discount is less than 100%. This reverses multiplication by the fraction of the marked price that remains. It does not add d% of the reduced price back to that price.

Worked example 5. An almirah is sold for ₹5,225 after a discount of 5%. This is the sale price before any tax calculation. Find its marked price.

Answer: The sale price is 95% of the marked price. Marked price = ₹5,225 × 100/95 = ₹5,500. Checking forwards, 5% of ₹5,500 is ₹275, and ₹5,500 − ₹275 = ₹5,225.

When the amount supplied includes GST as well as a discount, remove the GST first. Only then does the remaining amount represent the discounted fraction of the marked price. Reversing a sequence means undoing the last operation before undoing the earlier operation.

Thus, for a discount allowed before GST, M = 10000A/[(100 − d)(100 + r)]. The square brackets group the whole denominator. Use this combined expression only after identifying the meaning of each price in the question.

How do you extract GST from an inclusive amount?

An inclusive amount contains both the basic price and tax. Treating the basic price as 100 parts makes the relationship clear: the final amount contains 100 + r parts. Recovering the basic price therefore means taking 100 out of those 100 + r parts.

How does the unitary method work?

The unitary method finds the value of one unit or part first and then the required number of units. For an inclusive price, divide by the total number of percentage parts, then multiply by the parts representing the basic price or tax.

Worked example 6. Salim bought an article for ₹784 including GST of 12%. Find the price before GST and the GST amount.

Answer: The inclusive amount represents 112 parts and the basic price represents 100 parts. Basic price = ₹784 × 100/112 = ₹700. GST = ₹784 − ₹700 = ₹84. Checking, 12% of ₹700 is ₹84.

The GST amount is not 12% of ₹784. The supplied percentage refers to the basic price, which is ₹700. Replacing the base with the inclusive amount changes the question even though the rate written beside it remains the same.

How can subtraction check the tax?

Worked example 7. An article costs ₹1,239 including GST of 18%. Find its price before GST and the tax included.

Answer: Basic price = ₹1,239 × 100/118 = ₹1,050. GST = ₹1,239 − ₹1,050 = ₹189. Checking directly, ₹1,050 × 18/100 = ₹189, and ₹1,050 + ₹189 = ₹1,239.

Two checks now agree: the difference between total and basic price equals the tax, and the given percentage of the basic price equals that same tax. This checks both the arithmetic and the choice of percentage base.

If individual CGST and SGST amounts are required, their rates must also be known or their equal split specified. Recover B using the combined rate first, then calculate the components on B. Do not silently supply component rates missing from a question.

How do profit and loss connect with GST calculations?

Profit is the excess of selling price over cost price. Loss is the excess of cost price over selling price. These comparisons require a consistent cost basis; the GST-inclusive amount received from a buyer is not automatically the seller's sale value for calculating profit.

Let C denote cost price excluding GST in the problems considered here, and let S denote selling price excluding GST. For a sale without further adjustments, S is the taxable price B. Profit = S − C when S exceeds C; loss = C − S when C exceeds S.

How are profit and loss percentages applied?

Let p denote the numerical profit percentage and l the numerical loss percentage, both calculated on cost price. Then S = C(100 + p)/100 for profit, and S = C(100 − l)/100 for loss.

GST is then calculated on S. The total for a profit sale is A = C(100 + p)(100 + r)/10000. For a loss sale it is A = C(100 − l)(100 + r)/10000. These are successive percentage operations on different bases.

Worked example 8. Goods bought for ₹1,00,000 before GST are sold for ₹1,35,000 before GST in the same state. Take ₹1,00,000 as the cost basis, with no additional costs. The sale attracts CGST of 5% and SGST of 5%. Find profit, profit percentage and the buyer's total.

Answer: Profit = ₹1,35,000 − ₹1,00,000 = ₹35,000. Profit percentage = 35,000/1,00,000 × 100% = 35%. CGST and SGST are ₹6,750 each. The buyer's total is ₹1,35,000 + ₹6,750 + ₹6,750 = ₹1,48,500.

The profit percentage uses ₹1,00,000, while the tax percentages use ₹1,35,000. Labelling these bases explains why the three percentages cannot simply be added and applied to the cost price. Profit and GST describe different parts of the calculation.

Where additional expenses are included in cost price, account for them before calculating profit or loss. Do not invent expenses that the problem has not supplied. Equally, do not use a purchase total containing GST as a tax-exclusive cost without first establishing the intended cost basis.

How do you solve inverse cost-price and rate problems?

In an inverse cost-price problem, the consumer's payment may be the final result of both a profit or loss adjustment and GST. Separate these operations. First recover the selling price before GST; then recover the cost price from the stated profit or loss percentage.

How do you reverse profit or loss?

Using the symbols already defined, S = 100A/(100 + r). For profit calculated on cost, C = 100S/(100 + p). For loss calculated on cost, C = 100S/(100 − l), provided l is less than 100%.

These expressions give the combined inverse forms C = 10000A/[(100 + r)(100 + p)] for profit, and C = 10000A/[(100 + r)(100 − l)] for loss. Keep the brackets because each entire product forms a denominator.

The reasoning is more useful than memorising separate expressions. With a profit, the selling price represents more than the original hundred cost-price parts. With a loss, it represents fewer. Dividing by the appropriate multiplier restores the original cost.

How do you find an unknown GST rate?

If both basic price B and inclusive amount A are given, the tax is A − B. Hence r = 100(A − B)/B, with B positive. This compares the tax with the basic price, not with the final amount paid.

If the GST amount T and a positive rate r are given, B = 100T/r. The question has then supplied the tax part rather than the total, so dividing by 100 + r would use the wrong relationship.

Before solving, write a sentence identifying the known quantity: “This amount is tax”, “This amount includes tax”, or “This amount is before tax”. Those descriptions distinguish three superficially similar questions that require different operations.

Finally, insert the recovered quantity into the original forward calculation. An inverse answer is established when it reproduces the supplied total under the stated discount, profit or loss, and GST conditions.

How can you organise and check a complete GST solution?

A complete solution connects each percentage to its base and gives the quantity requested. A correct tax amount alone does not answer a question asking for the consumer's payment. Similarly, a correct inclusive price does not answer a request for the list price before discount.

What order should the working follow?

1. Read the price labels and identify whether each given amount includes or excludes GST.
2. Record the stated rates, distinguishing the total GST rate from its components.
3. For a forward problem, establish the taxable selling price after the specified discount or profit or loss calculation.
4. For an inverse problem, remove tax before reversing an earlier discount or profit or loss adjustment.
5. Calculate the requested amounts, state their units, and check by substitution into the forward relationship.

In a substitution check, put the calculated value back into the original relationship. For example, a recovered marked price must yield the stated sale price when its discount is taken off. A recovered basic price must yield the stated total when GST is added.

Which comparisons reveal a wrong base?

For positive prices and positive tax rates, adding GST produces a larger amount. Removing included GST produces a smaller basic price. A genuine discount reduces the marked price. These comparisons are useful checks, although they do not replace checking the actual arithmetic.

Keep exact fractions during inverse working when convenient, and apply any rounding instruction given in the question at the appropriate stage. Finish with the requested label, such as “CGST”, “marked price” or “amount paid”, so the final number has an unambiguous meaning.

Glossary

• Goods and Services Tax — A tax levied on the supply of goods or services or both.
• CGST — Central Goods and Services Tax, the central component in the same-state calculations considered here.
• SGST — State Goods and Services Tax, the state component in the same-state calculations considered here.
• Taxable value — The price on which the stated GST percentage is calculated.
• Tax-inclusive price — The amount containing both the basic price and the GST charged.
• Marked price — The stated list price before a discount is taken off.
• Discount — A reduction from marked price, with its percentage calculated on marked price.
• Cost price — The cost to the seller, using the cost basis specified in the problem.
• Selling price — The price at which an article is sold, distinguished here from the total including GST.
• Profit — The excess of selling price over cost price on a consistent basis.
• Loss — The excess of cost price over selling price on a consistent basis.
• Inverse calculation — A calculation that recovers an earlier quantity by reversing the operations applied to it.

Common errors and misconceptions

• Misconception: GST already included in a price is the stated percentage of that total. Correct: Recover the basic price by dividing the total by its tax multiplier, then subtract it from the total.
• Misconception: CGST must be added before SGST is calculated. Correct: Calculate both components on the same taxable price, then add the two tax amounts to that price.
• Misconception: A discount percentage is calculated on the discounted selling price. Correct: Its base is the marked price. Divide the reduction by the marked price when finding the discount percentage.
• Misconception: Adding the discount percentage to the reduced price restores the list price. Correct: Divide by the fraction of the list price remaining after discount; the two percentages would otherwise use different bases.
• Misconception: Discount and GST rates can be combined by simple subtraction. Correct: Discount acts on marked price, while GST acts on the resulting taxable price. Use successive multipliers.
• Misconception: The consumer's entire payment is the seller's price for calculating profit. Correct: For the tax-exclusive cost basis used here, remove GST before comparing selling price with cost price.
• Misconception: Example rates automatically apply to every similar item. Correct: Use the rates supplied for the particular calculation and distinguish each component rate from the total GST rate.

Exam-style questions with model answers

Q1. An article marked at ₹840 is sold for ₹714 before tax. Find the discount amount and discount percentage. [2 marks]

1. The discount is the reduction from marked price: ₹840 − ₹714 = ₹126.
2. The percentage base is ₹840, so discount percentage = 126/840 × 100% = 15%.

Q2. A computer printer costs ₹10,000 before GST. For this same-state sale, CGST is 5% and SGST is 5%. Calculate each component and the total payable. [3 marks]

1. CGST is calculated on the price before tax: ₹10,000 × 5/100 = ₹500. This is the central component of the tax.
2. SGST uses the same ₹10,000 base, so ₹10,000 × 5/100 = ₹500. It is not calculated after adding CGST.
3. Total payable = ₹10,000 + ₹500 + ₹500 = ₹11,000, including both GST components.

Q3. An article costs ₹1,239 including GST of 18%. Explain the percentage base, find the price before GST and the tax, and check the result. [4 marks]

1. The basic price represents 100 percentage parts. With GST of 18%, the supplied total represents 118 parts of that same basic price.
2. The price before GST is therefore ₹1,239 × 100/118 = ₹1,050.
3. The GST included is the difference between the two prices: ₹1,239 − ₹1,050 = ₹189.
4. Checking on the correct base, 18% of ₹1,050 is ₹189; adding this gives ₹1,239, the supplied inclusive amount.

Q4. An almirah sells for ₹5,225 after a 5% discount, before any tax calculation. Find the marked price and verify the discount. [3 marks]

1. A 5% discount leaves 95% of the marked price. Therefore the given ₹5,225 is the reduced price, not the base on which the discount percentage was calculated.
2. Marked price = ₹5,225 × 100/95 = ₹5,500. Division by the remaining fraction reverses the discount.
3. The discount is 5% of ₹5,500 = ₹275. Subtracting ₹275 from ₹5,500 gives ₹5,225, confirming the result.

Q5. Goods cost a seller ₹1,00,000 excluding GST and are sold for ₹1,35,000 excluding GST within the same state. Use ₹1,00,000 as the cost basis, with no additional costs. CGST and SGST on the sale are 5% each. Find profit, profit percentage, each GST amount and the buyer's total. [5 marks]

1. Profit is selling price less the specified cost price, both excluding GST. It is ₹1,35,000 − ₹1,00,000 = ₹35,000.
2. The profit percentage uses cost price as its base. It is 35,000/1,00,000 × 100% = 35%, rather than a percentage calculated on the sale total.
3. CGST uses the selling price before tax as its base: ₹1,35,000 × 5/100 = ₹6,750.
4. SGST is calculated independently on that same selling price: ₹1,35,000 × 5/100 = ₹6,750.
5. The buyer pays the selling price plus both components. The total is ₹1,35,000 + ₹6,750 + ₹6,750 = ₹1,48,500. The tax components do not form part of the profit calculated above.

Q6. Salim pays ₹784 for an article, including GST of 12%. Find the basic price and tax by percentage parts, verify the result, and explain why taking 12% of ₹784 is incorrect. [5 marks]

1. The GST rate refers to the basic price. Represent that basic price by 100 parts; adding GST of 12% makes the final amount 112 parts.
2. Since 112 parts equal ₹784, the basic price is ₹784 × 100/112 = ₹700. This reverses the addition of GST.
3. The tax is the difference between the inclusive amount and the basic price: ₹784 − ₹700 = ₹84.
4. As a forward check, ₹700 × 12/100 = ₹84. Adding this tax to ₹700 reproduces the supplied total of ₹784.
5. Taking 12% of ₹784 uses the total containing tax as the percentage base. The supplied rate applies to ₹700 instead, so that method cannot extract the tax included.

Key takeaways

• Identify whether every given price includes or excludes GST before choosing a direct or inverse calculation.
• Calculate the GST amount on the taxable price, then add it to obtain the consumer's total payment.
• Calculate CGST and SGST separately on the same taxable value, using the component rates supplied.
• For a discount allowed before GST, reduce the marked price first and calculate tax on the discounted price.
• To remove included GST, divide the final amount by the tax multiplier instead of subtracting its stated percentage.
• Profit and loss percentages use the specified cost price, while discount percentage uses the marked price.
• Reverse a sequence from its last operation, removing GST before recovering an earlier marked price or cost price.
• Check inverse answers by applying the original forward operations and confirming that they reproduce the supplied amount.

Test yourself

What does GST stand for, and what is it levied on?

GST stands for Goods and Services Tax. It is levied on the supply of goods or services or both.

Which price is the base for a discount percentage?

The marked or list price is the base, rather than the price after the discount.

A frock is marked at ₹220 with a 20% discount. What is its sale price before tax?

The discount is ₹44, so the sale price before tax is ₹220 − ₹44 = ₹176.

Railway transport costs ₹8,000 before CGST of 5% and SGST of 5%. What is the total?

Each component is ₹400. The total is ₹8,000 + ₹400 + ₹400 = ₹8,800.

Why do you divide an amount including 18% GST by 118 and multiply by 100?

The inclusive amount represents 118 parts, while the basic price represents 100 parts on the same percentage base.

Should SGST be calculated after CGST has been added?

No. In these split-tax calculations, both components are calculated independently on the same taxable price.

In a sale with a discount before GST, what must be undone first to recover the marked price?

Remove GST from the inclusive amount first, then reverse the discount using the fraction of marked price remaining.

Why must a profit calculation distinguish the sale price before GST from the buyer's total?

On the tax-exclusive cost basis used here, profit compares selling price before GST with cost price before GST.