Chapter 1: Value Added Tax (VAT & Goods and Services Tax - GST)

Tax is the primary source of revenue levied by Central and State Governments to meet administrative expenses, execute development schemes, and pay public salaries. In commercial transactions, taxation has evolved from single-point Sales Tax to Value Added Tax (VAT) and the unified Goods and Services Tax (GST). This master note covers all definitions, formula variations, overhead charges, consecutive discounts, multi-stage supply chain mechanics, SGST, CGST, IGST, direct and inverse GST cases, solved textbook examples, and board exam problems from the official ICSE Class 10 curriculum.

Official ICSE Class 10 Question Types Master Checklist

✔ Type 1: Basic Direct Tax Calculation — Given S.P. and Tax Rate %, find tax amount and final bill.
✔ Type 2: Single Trade Discount + Intra-State GST — Discount on Marked Price, split into CGST & SGST.
✔ Type 3: Consecutive / Successive Discounts + GST — Trade discount followed by off-season discount.
✔ Type 4: Multiple Goods Bill (Itemized Rates) — Different items with different GST rates & balance returned.
✔ Type 5: Overhead Expenses + Desired Profit + GST — Basic price + transport/repair overheads + profit %.
✔ Type 6: Inverse Case 1 (Finding M.P. from Total Bill) — Finding original price when final tax-inclusive bill is given.
✔ Type 7: Inverse Case 2 (Finding M.P. from SGST/CGST Amount) — Finding list price when SGST or CGST paid is given.
✔ Type 8: Multi-Stage Supply Chain Input Tax Credit (ITC) — Manufacturer → Wholesaler → Retailer → Consumer.
✔ Type 9: Inter-State Transaction (IGST Calculation) — Sales between different States/UTs ($\text{IGST} = \text{Full GST Rate}$).
✔ Type 10: Tax Rebate / Budget Discount Request — Extra discount needed so total bill inclusive of tax equals a target budget.

1. Fundamental Terms & Definitions

Commercial Definitions

Cost (Basic) Price (C.P.): The price at which a trader or customer purchases goods before adding overheads or taxes.
Selling Price (S.P.) / Sale Price: The price at which a trader sells goods to a customer, excluding tax.
Profit and Loss:
- $\text{Profit} = \text{S.P.} - \text{C.P.}$ and $\text{Profit Rate} = \frac{\text{Profit}}{\text{C.P.}} \times 100\%$
- $\text{Loss} = \text{C.P.} - \text{S.P.}$ and $\text{Loss Rate} = \frac{\text{Loss}}{\text{C.P.}} \times 100\%$
List Price / Marked Price (M.P.): The printed, quoted, or catalogue price of an article.
Discount: A reduction granted on the List Price / Marked Price. Discount is ALWAYS calculated on the Marked Price: $$\text{Discount Amount} = \frac{\text{Discount Rate}}{100} \times \text{Marked Price}$$
Sale Price after Discount: $$\text{Sale Price (S.P.)} = \text{Marked Price} - \text{Discount} = \text{M.P.} \times \left(1 - \frac{\text{Discount Rate}}{100}\right)$$ Note: If no discount is given, then $\text{Sale Price} = \text{Marked Price}$.

2. Computation of Sales Tax & Basic GST

Sales Tax or GST is calculated strictly as a percentage of the Sale Price (after all discounts are deducted).

$$\text{Sales Tax / GST Amount} = \frac{\text{Tax Rate}}{100} \times \text{Sale Price}$$ $$\text{Tax Rate} = \frac{\text{Sales Tax Amount}}{\text{Sale Price}} \times 100\%$$ $$\text{Total Price Paid by Customer} = \text{Sale Price} + \text{Sales Tax} = \text{Sale Price} \times \left(\frac{100 + x}{100}\right)$$

Reverse Calculation / Inverse Cases Formula

When the total bill amount (inclusive of tax rate $x\%$) is given, the original Sale Price (excluding tax) and Marked Price are found by:

$$\text{Sale Price} = \frac{\text{Total Price Inclusive of Tax} \times 100}{100 + x}$$ $$\text{Tax Amount} = \text{Total Price Inclusive of Tax} \times \frac{x}{100 + x}$$ $$\text{Marked Price} = \frac{\text{Sale Price} \times 100}{100 - \text{Discount Rate}}$$

3. Overhead Charges & Consecutive Discounts

Overhead Charges Rule

When a trader incurs extra expenses such as transportation, packing, labor, repairs, or finishing on an article before selling, these overheads are added directly to the purchase price to obtain the Total Cost Price:

$$\text{Total Cost Price (Effective C.P.)} = \text{Basic Purchase Price} + \text{Overhead Charges}$$

Profit or Loss percentage is always calculated on this Total Cost Price.

Consecutive / Off-Season Discounts

When two successive discounts $d_1\%$ (trade discount) and $d_2\%$ (off-season discount) are offered on a List Price (M.P.):

Price after 1st discount = $\text{M.P.} \times \left(1 - \frac{d_1}{100}\right)$
Final Sale Price = $\text{M.P.} \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right)$
Tax (GST/VAT) is charged on this Final Sale Price.

4. Value Added Tax (VAT) & GST Input/Output Credit

Unlike old single-point Sales Tax (collected only at the final point of retail sale), VAT / GST is a multi-stage tax collected at every transfer of goods from manufacturer to wholesaler, retailer, and consumer.

Core VAT / GST Input Credit Equation

Every dealer in the supply chain pays tax on their purchase (Input Tax) and collects tax on their sale (Output Tax). The dealer deposits only the difference with the government:

$$\text{VAT / GST Paid by Dealer} = \text{Output Tax} - \text{Input Tax}$$

where $\text{Output Tax} = \text{Tax Collected on Sale}$, $\text{Input Tax} = \text{Tax Paid on Purchase}$

$$\text{Net VAT / GST} = \frac{\text{Tax Rate}}{100} \times (\text{Selling Price} - \text{Cost Price})$$ $$\text{Net VAT / GST} = \frac{\text{Tax Rate}}{100} \times \text{Profit (Value Addition)}$$

Supply Chain Comparison Table (Rate of Tax = 10%)

Supply Stage	Purchase Price	Sale Price	Single-Point Sales Tax	VAT / GST Method
Manufacturer	₹600	₹1,000	Tax paid = Nil	Output Tax = ₹100, Input Tax = ₹60 VAT Paid = ₹40
1st Dealer (Wholesaler)	₹1,000	₹1,200	Tax paid = Nil	Output Tax = ₹120, Input Tax = ₹100 VAT Paid = ₹20
2nd Dealer (Retailer)	₹1,200	₹1,450	Tax paid = Nil	Output Tax = ₹145, Input Tax = ₹120 VAT Paid = ₹25
Final Customer	₹1,450	₹1,680	Sales Tax (10% of 1680) = ₹168	Output Tax = ₹168, Input Tax = ₹145 VAT Paid = ₹23
Total Revenue Received by Government			₹168	₹40 + ₹20 + ₹25 + ₹23 + ₹60 = ₹168

5. Modern Goods and Services Tax (GST): CGST, SGST & IGST Breakdown

Under the Goods and Services Tax (GST) system in India, taxes are classified based on the geographical jurisdiction of the commercial transaction:

1. Intra-State Sales (Within the Same State / Union Territory)

When goods or services are bought and sold within the same State or UT, the total GST rate is divided equally into two components:

Central Goods and Services Tax (CGST): Revenue goes to the Central Government. $$\text{CGST Rate} = \frac{\text{Total GST Rate}}{2}$$ $$\text{CGST Amount} = \frac{\text{CGST Rate}}{100} \times \text{Sale Price}$$
State Goods and Services Tax (SGST): Revenue goes to the State Government. $$\text{SGST Rate} = \frac{\text{Total GST Rate}}{2}$$ $$\text{SGST Amount} = \frac{\text{SGST Rate}}{100} \times \text{Sale Price}$$

$$\text{Total GST Paid} = \text{CGST Amount} + \text{SGST Amount}$$ $$\text{Total Price Paid by Consumer} = \text{Sale Price} + \text{CGST} + \text{SGST}$$

2. Inter-State Sales (Between Different States / UTs)

When goods or services are sold from one State/UT to another, a single unified tax is levied:

Integrated Goods and Services Tax (IGST): Collected entirely by the Central Government. $$\text{IGST Rate} = \text{Full GST Rate}$$ $$\text{IGST Amount} = \frac{\text{GST Rate}}{100} \times \text{Sale Price}$$ Note: In Inter-State transactions, $\text{CGST} = 0$ and $\text{SGST} = 0$.

Inverse GST Formulas Checklist (Finding Original Price from CGST/SGST)

If the amount of SGST or CGST paid is given as ₹$A$ at rate $r\%$ (where $r = \frac{\text{GST Rate}}{2}$):

$$\text{Sale Price (excluding tax)} = \frac{A \times 100}{r}$$ $$\text{Marked Price (if discount } d\% \text{ was given)} = \frac{\text{Sale Price} \times 100}{100 - d}$$

Transaction Type	Jurisdiction	CGST Rate	SGST Rate	IGST Rate	Total Tax Paid
Intra-State Sale	Same State / UT	$\frac{\text{GST Rate}}{2}$	$\frac{\text{GST Rate}}{2}$	0%	$\text{CGST} + \text{SGST}$
Inter-State Sale	Between Different States	0%	0%	Full GST Rate	$\text{IGST}$

6. Solved Master Examples Covering All 10 ICSE Question Types

Type 1 — Basic Sales Tax / GST Calculation

Problem: Rohit purchased a pair of shoes costing ₹850. Calculate the total amount to be paid by him if the rate of Sales Tax is 6%.

Solution:

Sale price = ₹850. Sales Tax = 6% of ₹850 = $\frac{6}{100} \times 850 =$ ₹51.

Total amount paid = ₹850 + ₹51 = ₹901.

Direct Method: Amount = ₹850 $\times \frac{100+6}{100} =$ ₹850 $\times 1.06 =$ ₹901.

Type 2 — Single Trade Discount + Intra-State GST (CGST + SGST)

Problem: The marked price of a Digital TV set is ₹20,000. A dealer allows a discount of 15% on the marked price. If the rate of GST is 18%, calculate: (i) Sale Price (excluding tax), (ii) CGST amount paid by consumer, (iii) SGST amount paid by consumer, (iv) Total amount paid by consumer.

Solution:

Marked Price = ₹20,000. Discount = 15% of ₹20,000 = ₹3,000.
(i) Sale Price (S.P.) = ₹20,000 - ₹3,000 = ₹17,000.
Since sale is intra-state, rate of CGST = $\frac{18\%}{2} = 9\%$, rate of SGST = $\frac{18\%}{2} = 9\%$.
(ii) CGST Amount = 9% of ₹17,000 = $\frac{9}{100} \times 17000 =$ ₹1,530.
(iii) SGST Amount = 9% of ₹17,000 = $\frac{9}{100} \times 17000 =$ ₹1,530.
(iv) Total Amount Paid by Consumer = Sale Price + CGST + SGST = ₹17,000 + ₹1,530 + ₹1,530 = ₹20,060.

Type 3 — Successive / Consecutive Discounts + GST (ICSE 2005)

Problem: The catalogue price of a computer set is ₹45,000. A shopkeeper gives a discount of 7% on listed price and a further off-season discount of 4% on the balance. Sales Tax at 8% is charged on the remaining amount. Find: (i) amount of Sales Tax customer pays, (ii) final price customer pays.

Solution:

List Price = ₹45,000. Discount 7% = ₹3,150 → Balance = ₹41,850.
Off-season discount 4% of ₹41,850 = ₹1,674 → Sale Price = ₹41,850 - ₹1,674 = ₹40,176.
(i) Sales Tax = 8% of ₹40,176 = ₹3,214.08.
(ii) Final Price paid = ₹40,176 + ₹3,214.08 = ₹43,390.08.

Type 4 — Multiple Itemized Goods Bill & Change Returned

Problem: Mrs. Sharma purchased confectionery costing ₹165 (Sales Tax 6%) and cosmetic goods costing ₹230 (Sales Tax 10%). If she gives a ₹500 note to the shopkeeper, what money will be returned to her?

Solution:

Price of confectionery incl. tax = ₹165 + 6% of ₹165 = ₹165 + ₹9.90 = ₹174.90
Price of cosmetics incl. tax = ₹230 + 10% of ₹230 = ₹230 + ₹23.00 = ₹253.00
Total amount to be paid = ₹174.90 + ₹253.00 = ₹427.90
Money returned by shopkeeper = ₹500 - ₹427.90 = ₹72.10

Type 5 — Overheads + Desired Profit % + GST

Problem: A trader buys an article for ₹3,600 and spends ₹1,200 on travelling and transportation. If he desires a profit of 15%, how much will a customer pay for the article if Sales Tax is 8%?

Solution:

Total Cost Price (C.P.) = ₹3,600 + ₹1,200 = ₹4,800
Sale Price (S.P.) = 115% of ₹4,800 = $\frac{115}{100} \times 4800 =$ ₹5,520
Sales Tax = 8% of ₹5,520 = ₹441.60
Money paid by customer = ₹5,520 + ₹441.60 = ₹5,961.60

Type 6 — Inverse Case 1: Finding M.P. from Total Bill (ICSE 2007)

Problem: Dinesh bought an article for ₹374, which included a discount of 15% on the marked price and a sales-tax of 10% on the reduced price. Find the marked price of the article.

Solution:

Let Marked Price = ₹$x$.

Sale Price after 15% discount = $x - \frac{15x}{100} = \frac{85x}{100}$.

Price inclusive of 10% tax = $\frac{85x}{100} \times \left(1 + \frac{10}{100}\right) = \frac{85x}{100} \times \frac{110}{100} = \frac{187x}{200}$.

Given $\frac{187x}{200} = 374 \implies x = 374 \times \frac{200}{187} = 400$.

Marked Price = ₹400.

Type 7 — Inverse Case 2: Finding M.P. from SGST/CGST Amount

Problem: A customer paid ₹540 as SGST on buying an article. If the rate of GST on the article is 12% and the dealer offered a discount of 10% on the list price, find: (i) CGST paid, (ii) Sale Price of article, (iii) Marked List Price of article.

Solution:

(i) Since CGST rate = SGST rate = $\frac{12\%}{2} = 6\%$, CGST Amount = SGST Amount = ₹540.
Let Sale Price = ₹$x$.
Then 6% of $x = 540 \implies \frac{6x}{100} = 540 \implies x = \frac{540 \times 100}{6} = 9000$.
(ii) Sale Price (excluding tax) = ₹9,000.
Let Marked Price = ₹$M$. Discount = 10%.
Sale Price = $M - 10\% \text{ of } M = \frac{90M}{100} = 9000 \implies M = \frac{9000 \times 100}{90} = 10000$.
(iii) Marked List Price = ₹10,000.

Type 8 — Multi-Stage Supply Chain Input Tax Credit (ICSE 2011)

Problem: A manufacturer sells a washing machine to a wholesaler for ₹15,000. The wholesaler sells it to a trader at a profit of ₹1,200 and the trader sells it to a consumer at a profit of ₹1,800. If VAT rate is 8%, find: (i) total VAT received by State Govt from manufacturer and wholesaler, (ii) total amount consumer pays.

Solution:

VAT from Manufacturer = 8% of ₹15,000 = ₹1,200.
Wholesaler C.P. = ₹15,000, S.P. = ₹16,200. Profit = ₹1,200.
VAT from Wholesaler = 8% of ₹1,200 = ₹96.
Trader S.P. to Consumer = ₹16,200 + ₹1,800 = ₹18,000.
Tax charged = 8% of ₹18,000 = ₹1,440.
Total Amount paid by Consumer = ₹18,000 + ₹1,440 = ₹19,440.

Type 9 — Inter-State Sale (IGST Calculation)

Problem: A manufacturer in Delhi sells goods worth ₹40,000 to a dealer in Punjab. If the rate of GST is 28%, calculate the IGST, CGST, SGST, and total bill amount.

Solution:

Since transaction is Inter-State (Delhi to Punjab), CGST = 0 and SGST = 0.
Rate of IGST = 28%.
IGST Amount = 28% of ₹40,000 = $\frac{28}{100} \times 40000 =$ ₹11,200.
Total Bill Amount = ₹40,000 + ₹11,200 = ₹51,200.

Type 10 — Tax Rebate / Budget Discount Request (Tricky ICSE Question)

Problem: The marked price of an article is ₹12,500. A customer wants to buy this article and requests the shopkeeper to give a discount on the marked price such that the total price inclusive of 12% GST equals the marked price. Find the discount amount the shopkeeper must allow.

Solution:

Let the reduced price (Sale Price) after discount = ₹$x$.
GST Rate = 12%. Price inclusive of tax = $x + 12\% \text{ of } x = \frac{112x}{100}$.
As per customer requirement, Tax-Inclusive Price = Marked Price = ₹12,500.
$$\frac{112x}{100} = 12500 \implies x = \frac{12500 \times 100}{112} = \text{₹}11,160.71$$
Required Discount Amount = $\text{Marked Price} - \text{Sale Price} = 12500 - 11160.71 =$ ₹1,339.29.

7. Formula Quick Reference Grid

Sale Price (S.P.)

$$\text{M.P.} - \text{Discount}$$

CGST & SGST Rate

$$\frac{\text{GST Rate}}{2}$$

(Intra-State Sale)

Total GST Bill

$$\text{S.P.} + \text{CGST} + \text{SGST}$$

Net VAT / GST

$$\text{Output Tax} - \text{Input Tax}$$

Inverse Sale Price

$$\frac{\text{Total Bill} \times 100}{100 + \text{GST Rate}}$$

Inverse Marked Price

$$\frac{\text{S.P.} \times 100}{100 - \text{Discount Rate}}$$

8. Comprehensive ICSE Board Practice Problems

Textbook Exercises & Past Board Questions

Q1 (ICSE 2003). The price of a washing machine, inclusive of Sales Tax, is ₹13,530. If the Sales Tax is 10%, find its basic (cost) price.

Solution:
Basic Price = $\frac{13530 \times 100}{100 + 10} = \frac{1353000}{110} =$ ₹12,300.

Q2 (ICSE 2002). The price of a T.V. set inclusive of Sales Tax of 9% is ₹13,407. Find its marked price. If Sales Tax is increased to 13%, how much more does the customer have to pay?

Solution:
Marked Price = $\frac{13407 \times 100}{109} =$ ₹12,300.
New Tax at 13% = 13% of ₹12,300 = ₹1,599.
New Total Price = ₹12,300 + ₹1,599 = ₹13,899.
Extra amount customer pays = ₹13,899 - ₹13,407 = ₹492.

Q3 (ICSE 2014). A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price being ₹18,000. The shopkeeper sells it to a consumer at a discount of 10% on printed price. If VAT is 8%, find: (i) VAT paid by shopkeeper, (ii) total amount consumer pays.

Solution:
Shopkeeper C.P. = ₹18,000 - 20% of ₹18,000 = ₹14,400.
Consumer C.P. (Shopkeeper S.P.) = ₹18,000 - 10% of ₹18,000 = ₹16,200.
Input Tax = 8% of ₹14,400 = ₹1,152.
Output Tax = 8% of ₹16,200 = ₹1,296.
(i) VAT paid by shopkeeper = ₹1,296 - ₹1,152 = ₹144 (or 8% of (₹16,200 - ₹14,400) = ₹144).
(ii) Total amount paid by consumer = ₹16,200 + ₹1,296 = ₹17,496.

Q4 (ICSE 2015). A wholesaler buys a TV from the manufacturer for ₹25,000. He marks the price of the TV 20% above his cost price and sells it to a retailer at 10% discount on marked price. If VAT rate is 8%, find: (i) marked price, (ii) retailer's cost price inclusive of tax, (iii) VAT paid by wholesaler.

Solution:
(i) Marked Price = ₹25,000 + 20% of ₹25,000 = ₹30,000.
Retailer S.P. = ₹30,000 - 10% of ₹30,000 = ₹27,000.
Tax on Retailer purchase = 8% of ₹27,000 = ₹2,160.
(ii) Retailer's cost price inclusive of tax = ₹27,000 + ₹2,160 = ₹29,160.
Wholesaler Input Tax = 8% of ₹25,000 = ₹2,000.
Wholesaler Output Tax = 8% of ₹27,000 = ₹2,160.
(iii) VAT paid by wholesaler = ₹2,160 - ₹2,000 = ₹160.

Q5 (ICSE 2012). The printed price of an article is ₹60,000. The wholesaler allows a discount of 20% to the shopkeeper. The shopkeeper sells the article to the customer at the printed price. Sales tax (under VAT) is charged at 6% at every stage. Find: (i) cost to shopkeeper inclusive of tax, (ii) VAT paid by shopkeeper to Government, (iii) cost to customer inclusive of tax.

Solution:
Wholesaler S.P. (Shopkeeper C.P.) = ₹60,000 - 20% = ₹48,000.
Tax paid by shopkeeper = 6% of ₹48,000 = ₹2,880.
(i) Cost to shopkeeper inclusive of tax = ₹48,000 + ₹2,880 = ₹50,880.
Shopkeeper S.P. = ₹60,000 → Tax charged = 6% of ₹60,000 = ₹3,600.
(ii) VAT paid by shopkeeper = ₹3,600 - ₹2,880 = ₹720.
(iii) Cost to customer inclusive of tax = ₹60,000 + ₹3,600 = ₹63,600.