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Class 10 Exam  >  Class 10 Notes  >  Mathematics Class 10 ICSE  >  Chapter Notes: Value Added Tax

Value Added Tax Chapter Notes | Mathematics Class 10 ICSE PDF Download

IntroductionValue Added Tax - Class 10 ICSE Mathematics Notes

Imagine walking into a store to buy your favourite gadget or a pair of shoes, and the final price is slightly higher than expected due to something called "tax." Ever wondered why this happens and how it works? Welcome to the world of Value Added Tax (VAT) and Sales Tax! In this chapter, we'll unravel the mystery behind these taxes, which help governments fund everything from roads to schools. We'll explore how taxes are calculated on the goods we buy, how discounts and overheads affect prices, and how VAT is a smarter way to collect taxes at every step of a product's journey from the factory to your hands. Get ready to dive into some simple math that powers the economy!

Value Added Tax Chapter Notes | Mathematics Class 10 ICSE

Governments (state and central) need funds for:

  • Administrative expenses.
  • Welfare and development schemes.
  • Salaries of employees.

State governments collect revenue through a tax on the sale of goods within their region, called Sales Tax or Trade Tax.
The central government levies Central Sales Tax (C.S.T) on goods moving between states.

Example: A state government collects Sales Tax on a TV sold within its borders, while the central government collects C.S.T. if the TV is shipped from one state to another.

Some Important Terms

  • Cost Price (C.P.) or Basic Price: The price at which a trader buys goods.
  • Selling Price (S.P.) or Sale Price: The price at which a trader sells goods, excluding any tax.
  • Profit or Loss:
    • Profit = S.P. - C.P.
    • Loss = C.P. - S.P.
    • Profit % = (Profit / C.P.) × 100%
    • Loss % = (Loss / C.P.) × 100%
  • List Price (Marked Price, M.P.): The price marked on an article, also called printed price or quoted price.
  • Discount:A percentage reduction offered on the list price to clear old stock or for other reasons, calculated on the marked price.
    • If no discount is given, Sale Price = Marked Price.

Example: A trader buys a shirt for ₹500 (C.P.) and sells it for ₹600 (S.P.). The profit is ₹600 - ₹500 = ₹100. The profit percentage is (100 / 500) × 100% = 20%.

Computation of Sales Tax

  • Sales Tax is calculated on the Sale Price.
  • Sales Tax = (Rate of Sales Tax × Sale Price) / 100
  • Rate of Sales Tax = (Sales Tax / Sale Price) × 100%
  • Total Amount Paid by Customer: Sale Price + Sales Tax (if applicable).
  • Rates of Sales Tax vary based on the type of goods and differ across states.
  • Some essential or daily-use items may be fully or partially exempt from Sales Tax.

Example 1: Rohit buys shoes costing ₹850 with a Sales Tax rate of 6%.

  • Step 1: Calculate Sales Tax = 6% of ₹850 = (6 / 100) × 850 = ₹51.
  • Step 2: Total amount = Sale Price + Sales Tax = ₹850 + ₹51 = ₹901.
  • Direct Method: Total amount = ₹850 × (100 + 6) / 100 = ₹850 × 1.06 = ₹901.

Example 2: Mr. Gupta buys an article for ₹702, including 8% Sales Tax. Find the Sale Price.

  • Step 1: Let Sale Price = ₹x.
  • Step 2: Total price = x + 8% of x = x + (8 / 100)x = 1.08x.
  • Step 3: Given 1.08x = 702.
  • Step 4: x = 702 × 100 / 108 = ₹650.
  • Direct Method: Sale Price = ₹702 × 100 / (100 + 8) = ₹702 × 100 / 108 = ₹650.
  • Answer: Sale Price = ₹650.

Example 3: The total price of face-cream is ₹79.10, including Sales Tax, with a printed price of ₹70. Find the Sales Tax rate.

  • Step 1: Sales Tax = Total Price - Printed Price = ₹79.10 - ₹70 = ₹9.10.
  • Step 2: Rate of Sales Tax = (Sales Tax / Printed Price) × 100% = (9.10 / 70) × 100% = 13%.
  • Answer: Rate of Sales Tax = 13%.

 Problems Involving Overhead Charges and Discounts

  • Overhead Charges: Additional expenses like transportation, packing, etc., added to the Cost Price.
  • Total Cost Price: Cost Price + Overhead Charges.
  • Sale Price with Profit: Calculated as (100 + Profit%) / 100 × Total Cost Price.
  • Discounts: Applied sequentially on the Marked Price to get the Sale Price.
  • Customer’s Final Price: Sale Price + Sales Tax.

Example 1: A trader buys an article for ₹3,600 (including taxes) and spends ₹1,200 on overheads. He wants a 15% profit, and the customer pays 8% Sales Tax.

  • Step 1: Total Cost Price = ₹3,600 + ₹1,200 = ₹4,800.
  • Step 2: Sale Price = (100 + 15) / 100 × ₹4,800 = 115 / 100 × ₹4,800 = ₹5,520.
  • Step 3: Sales Tax = 8% of ₹5,520 = (8 / 100) × ₹5,520 = ₹441.60.
  • Step 4: Customer’s Price = ₹5,520 + ₹441.60 = ₹5,961.60.

Example 2: The catalogue price of a computer is ₹45,000. A shopkeeper gives a 7% discount, then a 4% off-season discount, with 8% Sales Tax on the remaining amount. Find the Sales Tax and final price.

  • Step 1: Discount = 7% of ₹45,000 = ₹3,150.
  • Step 2: Price after discount = ₹45,000 - ₹3,150 = ₹41,850.
  • Step 3: Off-season discount = 4% of ₹41,850 = ₹1,674.
  • Step 4: Sale Price = ₹41,850 - ₹1,674 = ₹40,176.
  • Step 5: Sales Tax = 8% of ₹40,176 = ₹3,214.08.
  • Step 6: Final Price = ₹40,176 + ₹3,214.08 = ₹43,390.08.
  • Answer: Sales Tax = ₹3,214.08, Final Price = ₹43,390.08.

Example 3: Dinesh buys an article for ₹374, including a 15% discount and 10% Sales Tax on the reduced price. Find the Marked Price.

  • Step 1: Let Marked Price = ₹100.
  • Step 2: Discount = 15% of ₹100 = ₹15, Sale Price = ₹100 - ₹15 = ₹85.
  • Step 3: Sales Tax = 10% of ₹85 = ₹8.50, Total Price = ₹85 + ₹8.50 = ₹93.50.
  • Step 4: If Total Price = ₹93.50, Marked Price = ₹100.
  • Step 5: For Total Price = ₹374, Marked Price = (100 / 93.50) × ₹374 = ₹400.
  • Alternative Method: Let Marked Price = ₹x.
  • Discount = 15% of x = (15 / 100)x = 3x / 20.
  • Sale Price = x - 3x / 20 = 17x / 20.
  • Total Price = (17x / 20) × (100 + 10) / 100 = 187x / 200.
  • Given 187x / 200 = 374, so x = 374 × 200 / 187 = ₹400.
  • Direct Method: ₹374 = M.P. × (85 / 100) × (110 / 100), M.P. = ₹374 × (100 / 85) × (100 / 110) = ₹400.
  • Answer: Marked Price = ₹400.

Value Added Tax (VAT)

  • VAT is a method of collecting tax on the sale/purchase of goods at every stage, from manufacturer to retailer.
  • It replaces the traditional Sales Tax, which was collected at a single point.
  • VAT is collected by state governments.
  • VAT Formula: VAT = Tax recovered on sale - Tax paid on purchase.
  • VAT is the tax on the value added at each transfer of goods.
  • Value Added: Difference between Selling Price and Cost Price at each stage.
  • Total VAT collected across all stages equals the Sales Tax paid by the final customer.

Example 1: A trader buys an article for ₹800 with 10% tax and sells it for ₹1,150 with 10% tax.

  • Step 1: Tax paid = 10% of ₹800 = ₹80.
  • Step 2: Tax charged = 10% of ₹1,150 = ₹115.
  • Step 3: VAT = ₹115 - ₹80 = ₹35.
  • Alternative Method: Value Added = ₹1,150 - ₹800 = ₹350, VAT = 10% of ₹350 = ₹35.

Example 2: A shopkeeper buys an article for ₹1,400 (after 30% discount on ₹2,000 printed price) with 8% tax and sells it at the printed price with 8% tax. Find the VAT paid.

  • Step 1: Discount = 30% of ₹2,000 = ₹600, Cost Price = ₹2,000 - ₹600 = ₹1,400.
  • Step 2: Tax paid = 8% of ₹1,400 = ₹112.
  • Step 3: Selling Price = ₹2,000, Tax charged = 8% of ₹2,000 = ₹160.
  • Step 4: VAT = ₹160 - ₹112 = ₹48.
  • Alternative Method: VAT = Tax on S.P. - Tax on C.P. = 8% of ₹2,000 - 8% of ₹1,400 = ₹160 - ₹112 = ₹48.
  • Third Method: Value Added = ₹2,000 - ₹1,400 = ₹600, VAT = 8% of ₹600 = ₹48.
  • Answer: VAT = ₹48.

Example 3: A shopkeeper sells an article for ₹7,500 with 12% tax and pays ₹180 VAT. Find the price (including tax) paid by the shopkeeper.

  • Step 1: Tax charged = 12% of ₹7,500 = ₹900.
  • Step 2: VAT = Tax charged - Tax paid, so ₹180 = ₹900 - Tax paid.
  • Step 3: Tax paid = ₹900 - ₹180 = ₹720.
  • Step 4: If Cost Price = ₹x, Tax paid = 12% of x = ₹720, so x = ₹720 × 100 / 12 = ₹6,000.
  • Step 5: Price including tax = ₹6,000 + ₹720 = ₹6,720.
  • Alternative Method: Price including tax = ₹6,000 + 12% of ₹6,000 = ₹6,000 + ₹720 = ₹6,720.
  • Answer: Price including tax = ₹6,720.
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FAQs on Value Added Tax Chapter Notes - Mathematics Class 10 ICSE

1. What is Value Added Tax (VAT) and how does it differ from sales tax?
Ans.Value Added Tax (VAT) is a consumption tax levied on the value added to goods and services at each stage of production or distribution. Unlike sales tax, which is charged only at the final sale to the consumer, VAT is collected at every stage of the supply chain, meaning that businesses pay VAT on their purchases and charge VAT on their sales. This allows for a more transparent tax system, as businesses can reclaim the VAT paid on their inputs.
2. How is the computation of sales tax typically performed?
Ans.Computation of sales tax involves determining the taxable amount of a sale and applying the appropriate tax rate. The formula used is: Sales Tax = Taxable Amount x Tax Rate. Businesses must keep accurate records of their sales and the sales tax collected, which is then reported and remitted to the tax authorities periodically.
3. What are overhead charges, and how do they affect pricing?
Ans.Overhead charges refer to the indirect costs associated with running a business, such as rent, utilities, and salaries of non-production staff. These costs must be factored into the pricing of goods and services to ensure that the business remains profitable. By including overhead charges in the pricing strategy, businesses can cover their fixed costs while also achieving their desired profit margins.
4. How do discounts impact the calculation of VAT?
Ans.Discounts can affect the calculation of VAT as they lower the taxable amount of a sale. When a discount is applied, the VAT is calculated on the reduced price rather than the original price. This means that both the seller and the buyer benefit from the discount, as the seller collects less VAT, and the buyer pays less overall. Accurate record-keeping of discounts is crucial for proper VAT reporting.
5. Why is it important for businesses to understand VAT regulations?
Ans.Understanding VAT regulations is crucial for businesses as non-compliance can lead to penalties, fines, and legal issues. Additionally, correct knowledge of VAT allows businesses to accurately charge and collect tax, reclaim input VAT, and maintain proper financial records. Staying informed about VAT changes ensures that businesses remain compliant and can effectively manage their financial obligations.
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