Value Added Tax Class 10 ICSE — Bansal Chapter 1
Chapter 1 of the Bansal ICSE Class 10 Mathematics book teaches Value Added Tax, or VAT. It begins with Sales Tax and Trade Tax, the taxes states levy on goods sold inside their borders. The chapter then builds the formulas for computing tax on a sale price. Later sections add overhead charges, discounts, and the VAT system itself. This page explains each section in order, with worked patterns and the chapter PDF.
ICSE Class 10 Mathematics Bansal Chapter 1 Value Added Tax PDF
What is inside Chapter 1
14 pages · 5 sections · 11 worked examples · 13 exercise questions
| Section | Title |
|---|---|
| 1.1 | Introduction |
| 1.2 | Some Important Terms |
| 1.3 | Computation of Sales Tax |
| 1.4 | Problems Involving Overhead Charges and Discounts |
| 1.5 | Value – Added Tax (VAT) |
- EXERCISE 1(A): 13 questions
1.1 Introduction
Governments need money to run the country. The chapter lists three reasons: administrative expenses, welfare and development schemes, and salaries of employees. To collect this revenue, state governments levy tax on the sale of goods inside their territory. That tax is called Sales Tax or Trade Tax.
When goods move from one state to another, the Union Government levies a separate tax. It is called Central Sales Tax, or C.S.T. So the name of the tax depends on where the sale takes place. A sale inside a state attracts Sales Tax. A sale across state lines attracts C.S.T.
This distinction matters for the rest of the chapter. Every later formula uses the sale price and the tax rate, whichever tax name applies. The computation is identical. Only the collecting authority changes. You can verify the current Class 10 Mathematics syllabus on the official CISCE website. This page sits inside the Class 10 Mathematics book collection on icseboard.org.
1.2 Some Important Terms
This section fixes the vocabulary used throughout the chapter. Cost Price (C.P.) is the price a trader pays to buy goods, also called the basic price. Selling Price (S.P.) is the price at which the trader sells the goods, before any tax is added. List Price is the marked or printed price of the article.
The profit and loss formulas come next:
\text{Profit} = \text{S.P.} - \text{C.P.}, \quad \text{Loss} = \text{C.P.} - \text{S.P.}
\text{Profit}\% = \frac{\text{Profit}}{\text{C.P.}} \times 100\%, \quad \text{Loss}\% = \frac{\text{Loss}}{\text{C.P.}} \times 100\%
Discount is a percentage of the list price. Shopkeepers give it to clear old stock or for other reasons. The discount is always calculated on the marked price. When an article sells without any discount, its sale price equals its marked price.
These five terms appear in every question in the chapter. A trader’s profit percent is always calculated on the cost price, never on the sale price. That rule is easy to forget in a tax question, so keep it in mind.
1.3 Computation of Sales Tax
This section states three rules for sales tax. First, Sales Tax is calculated on the Sale Price, not on the marked price or cost price. Second, the tax amount comes from the rate times the sale price. Third, the rate itself can be recovered by reversing the calculation.
The rules in formula form:
\text{Sales Tax} = \frac{\text{Rate of Sales Tax} \times \text{Sale Price}}{100}
\text{Rate of Sales Tax} = \frac{\text{Sales Tax}}{\text{Sale Price}} \times 100\%
If the rate is x\%, the price paid is the sale price multiplied by \frac{100+x}{100}. This is the direct method. The customer’s total is always the sale price plus the tax on it.
Worked pattern: an article sells for ₹2,400 at 5% tax. The tax is \frac{5}{100} \times 2400 = ₹120, so the customer pays ₹2,520. Reverse case: a total of ₹1,134 at 8% tax gives a sale price of \frac{1134 \times 100}{108} = ₹1,050. The tax is ₹84.
Rates differ by state and by item. Some necessities of daily use are fully or partially exempt. The chapter notes this so students do not assume one rate for every good.
1.4 Problems Involving Overhead Charges and Discounts
This section combines the earlier ideas in a fixed order. First, overhead charges join the purchase price to give the true cost price. Second, the desired profit is computed on that cost price. Third, sales tax is charged on the final sale price.
The multiplier form is useful:
\text{Sale-price} = \text{C.P.} \times \frac{100 + \text{Profit}\%}{100}
Worked pattern: a trader pays ₹2,000 for an article and spends ₹400 on transport. The true C.P. is ₹2,400. A desired 20% profit makes the sale price \frac{120}{100} \times 2400 = ₹2,880. The customer pays ₹2,880 plus 8% tax, which is ₹230.40, so the total is ₹3,110.40.
Discounts work on the balance. Each discount is taken on the price after the previous discount. Pattern: a list price of ₹30,000 gets a 10% discount, then 5% on the balance. The price becomes 30000 \times 0.90 \times 0.95 = ₹25,650. An 8% tax gives a final price of 25650 \times 1.08 = ₹27,702.
When both discount and tax are given, three methods find the marked price:
| Method | How it works |
|---|---|
| Assume ₹100 | Set M.P. = ₹100, apply discount and tax, scale the result to the given price |
| Algebra with x | Let M.P. = x, form one equation, solve for x |
| Direct multiplier | Price paid = M.P. × (100−d)/100 × (100+t)/100, then rearrange |
All three give the same answer. Common mistakes: applying tax before the discount, adding overheads after computing profit, and taking each successive discount on the original list price. Fix the order of steps first:
- Add overheads to the purchase price to get the true C.P.
- Apply discounts to the list price, each on the balance.
- Compute profit on the C.P. to get the sale price.
- Add sales tax to the sale price for the customer’s total.
1.5 Value – Added Tax (VAT)
VAT replaces the old single-point sales tax. In the old system, only one seller — manufacturer, wholesaler, or retailer — paid the tax. Under VAT, the government collects tax at every stage from manufacturer to retailer. Each stage deposits only the tax on the value it added.
The core identity:
\text{VAT} = \text{Tax recovered on sale} - \text{Tax paid on purchase}
equivalently,
\text{VAT} = \text{Rate} \times (\text{S.P.} - \text{C.P.})
Worked pattern: a dealer buys at ₹5,000 and pays 10% tax, which is ₹500. He sells at ₹6,500 and charges 10% tax, which is ₹650. The VAT is ₹650 − ₹500 = ₹150. The same result comes from 10% of ₹1,500, the value added.
Multi-stage chain: manufacturer sells at ₹8,000, wholesaler at ₹10,000, retailer at ₹12,000, all at 10%. VAT is ₹800, ₹200, and ₹200. The sum, ₹1,200, equals 10% of the customer’s price of ₹12,000. This telescoping property is why VAT totals match the old single-point tax.
Edge case: goods exempted from tax are not part of the taxable turnover. The chapter’s example has a shopkeeper with ₹45,000 of exempt sales, which are simply left out of the tax calculation. You can explore the other chapters of this book, such as Banking, in the Class 10 Mathematics section.
What to practise from this chapter
The chapter has one exercise block, EXERCISE 1(A), with 13 questions. In these questions, all prices are excluding tax unless stated.
- EXERCISE 1(A) — 13 questions
Several questions are tagged with the year of an earlier ICSE board paper, such as 2001, 2002, 2003, 2005, 2007, 2008, 2010, 2011, 2013, 2014, and 2015. Practising these gives a feel for the exam style. The full list of chapters sits in the Class 10 book index.
Frequently asked questions
What is the difference between Sales Tax and VAT?
Sales Tax is collected at a single point, usually by the retailer. VAT is collected at every stage from manufacturer to retailer. Each stage deposits only the tax on the value it added, so the total matches the single-point tax.
Is VAT calculated on the selling price or on the value added?
Both. VAT equals the tax charged on the sale minus the tax paid on the purchase. It also equals the tax rate times (S.P. − C.P.), which is the value added. The two forms give the same number.
Does discount come before or after adding sales tax?
Discount comes first. The discount reduces the marked price to the sale price, and sales tax is charged on that reduced price. Applying tax before the discount gives a wrong, higher answer.
How do overhead charges change the cost price of an article?
Overheads such as transport and packing are added to the purchase price. The true cost price is purchase price plus overheads. Profit is then computed on this true cost price, not on the purchase price alone.
How do I find the marked price when the final price includes both discount and tax?
Use one of three methods: assume the marked price is ₹100 and scale up, set it as x and solve an equation, or use the direct multiplier. All three give the same answer.
Reference: ICSE Class 10 Mathematics textbook material, chapter 1: Value Added Tax — CISCE-aligned.
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