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GST questions in ICSE Class 10 maths look like arithmetic, but marks are usually lost on the set-up: which price the tax is on, how to split it, and what a dealer actually pays the government. This post covers what the syllabus asks, the one idea behind input tax credit, and three worked examples, including a reverse problem.
What does the ICSE syllabus ask about GST?
The ICSE 2027 Mathematics syllabus puts Goods and Services Tax first under Commercial Mathematics in Class X. It asks for computation of tax "including problems involving discounts, list-price, profit, loss, basic/cost price including inverse cases", and for the price paid by the consumer after paying State GST and Central GST. The rates will be provided in the question, so you never need to memorise rates for particular goods. The syllabus does not use the phrase input tax credit, but you need the idea for any question that follows one article through several sellers.
How does GST split between CGST and SGST?
The CBIC's About GST page describes GST as levied "at all stages right from manufacture up to final consumption with credit of taxes paid at previous stages available as setoff", so that "only value addition will be taxed and burden of tax is to be borne by the final consumer". Its GST overview describes concurrent levy by the Centre (CGST) and the States (SGST), and IGST on inter-State supplies.
For ICSE problems this gives three rules:
Sale within one state: GST is split equally. At 18%, CGST is 9% and SGST is 9%.
Sale between states: the whole rate is IGST.
Discounts come first: find the selling price after any discount, then charge GST on it.
What is input tax credit?
When a dealer buys goods, they pay GST to their supplier. When they sell, they collect GST from their buyer. They pay the government only the difference:
GST payable = output tax (collected on sale) − input tax (paid on purchase)
Worked example 1: one article, three sellers, one state
A manufacturer sells a machine to a wholesaler for ₹20,000. The wholesaler sells it to a retailer for ₹24,000, and the retailer sells it to a customer for ₹30,000. All sales are in one state, and GST is 18%.
Manufacturer: output tax = 18% of 20,000 = ₹3,600. No input tax, so they pay ₹3,600 (CGST ₹1,800 + SGST ₹1,800).
Wholesaler: output tax = 18% of 24,000 = ₹4,320. Input tax = ₹3,600. Payable = ₹720 (CGST ₹360 + SGST ₹360).
Retailer: output tax = 18% of 30,000 = ₹5,400. Input tax = ₹4,320. Payable = ₹1,080 (CGST ₹540 + SGST ₹540).
Customer pays 30,000 + 5,400 = ₹35,400.
Check: 3,600 + 720 + 1,080 = ₹5,400, exactly the tax the customer paid. Another check: the wholesaler added ₹4,000 of value and paid 18% of 4,000 = ₹720; the retailer added ₹6,000 and paid ₹1,080.
Worked example 2: a discount, then GST
An article is marked at ₹5,000. The shop gives 10% discount, and GST is 12% in an intra-state sale.
Selling price = 5,000 − 500 = ₹4,500.
GST = 12% of 4,500 = ₹540, so CGST = ₹270 and SGST = ₹270.
Amount paid = 4,500 + 540 = ₹5,040.
Worked example 3: the inverse case
An article marked at ₹2,500 has GST at 12%. A customer can pay only ₹2,016 including GST. What discount percent must the shop give?
Let the price after discount be x. Then x + 12% of x = 2,016, so 1.12x = 2,016 and x = ₹1,800.
Discount = 2,500 − 1,800 = ₹700.
Discount percent = 700 / 2,500 × 100 = 28%.
The ICSE 2027 specimen paper has a question of exactly this shape, with an 18% rate, and its marking scheme starts the same way: let the reduced price be x and write x + 18% of x equal to the amount paid.
Common mistakes and how to avoid them
Charging GST on the marked price when a discount is given. Discount first, then tax.
Splitting IGST. Only intra-state GST is split into CGST and SGST.
Taking 12% off a tax-inclusive price to find the base. Divide by 1.12; 12% of the tax-inclusive price is too large.
Adding up every dealer's output tax and calling it the tax paid to the government. Subtract input tax at each stage.
A practice routine for GST
Do one forward and one reverse problem each day for a week. For chain problems, draw a row of boxes, one per seller, and write purchase price, sale price, output tax, input tax and tax payable in each box, then run the quick check. Mix in recurring deposit and shares questions so you practise choosing the method; research on mixed practice by Rohrer and Taylor (2007) found students did far better a week later after mixed rather than blocked practice. Our ICSE Class 10 maths paper guide shows where commercial maths sits in the paper.
When a reverse problem will not come out, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
Try it now: redo worked example 1 with GST at 5% and confirm that the stage payments add up to the customer's tax.
