# What is VAT in Maths?

VAT is short for value-added tax.

Due to a new method of realizing tax on goods purchased or sold, we already know about the tax. The government used to realize sales tax at a single point in the past.

Manufacturers and importers of goods (wholesalers and stockists) were responsible for paying government sales taxes. From the manufacturer to the retailer, the government realizes value-added tax at numerous points in the supply chain. During each stage, sales tax is applied only to the value added. Consumers are ultimately responsible for paying sales tax.

Also, read What is £600 plus VAT?

Each time goods are transferred, taxes are calculated by comparing the manufacturer’s original price with the retailer’s original price.

For example, if a trader purchases a product for $800 and the tax rate is 10%, he will pay$ 80 in taxes.

The same article can now be sold for $1150. His tax recovery (get) = 10% of 1150 =$115

VAT = Revenue from the sale – revenue from the purchase

= $115 –$ 80 = $35 Let’s assume that a retailer buys an item for$100 from a wholesaler. As prescribed by the government for that variety of articles, the wholesaler charges a 10% sales tax on it. As a result, the retailer must pay the wholesaler $100 + 10% of$100, or $100 +$10 (equals $110). Sales tax of$10 is paid to the government by the wholesaler, who receives $100. According to government regulations, the retailer charges 10% sales tax on the article sold to the consumer for$120. For example, the consumer pays the retailer $120 + 10% of$120, or $120 +$12 (equivalent to $132). Once the retailer pays the government$2 as sales tax, he gets $120 +$10, or $130. The retailer pays the government 10% of the sale price minus the cost price, or ($120 – $100). Retailers pay tax on the value that has been added to the article, or on its increased value. As a result, the retailer in this case will pay$2 in value added tax.

Also, read What is £500 plus VAT?

Here is a summary of the above example so that you can better understand it.

We have the following retailers;

The price of the purchase is $100 An input tax of$10 is paid on purchases.

The sale price is $120 Output tax =$12. (This tax is known as tax on the sale price)

Credit for input tax = $10 As a result, value added tax payable by the retailer = output tax – input tax =$12 – $10 =$2

Note: Value added tax (VAT) = output tax – input tax

Also, read VAT Threshold

## Examples

Example: Retailers buy an article at Rs 80 from wholesalers, and the wholesaler charges 8% sales tax. At the same time, the retailer charges sales tax of Rs 100. In order to answer the following question, you will need to apply the VAT system of calculating sales tax.

(i) How much does the article cost?

(ii) Determine the retailer’s input and output taxes.

(iii) What is the retailer’s VAT payment?

Solution:

(i) In this case, P equals 100 rupees, and r% equals 8% of the price.

Consumer cost price

(ii) Input tax = Retailer’s tax paid to wholesaler

Consumer-side output tax = Retailer-side output tax

(iii) Retailer’s VAT = Output tax – Input tax

=Rs (8-6.40)

=Rs 1.60

Example 2: An article that costs Rs 1500 is sold by a shopkeeper and charged sales tax at 12% to the customer. At what price inclusive of tax did the shopkeeper purchase the article from the wholesaler if he paid a VAT of Rs 36 to the government?

Solution:

Output tax = tax recouped by the retailer from the consumer

Before tax, let P be the wholesaler’s price for the article.

Then the input tax

Now,

VAT= Output tax  -Input tax

P= Rs 1200

the required price=P+ input tax= Rs (1200+144) = Rs 1344

Example 3: A manufacturer printed a price of 120 rupees per article on the packaging of his goods. In turn, the wholesaler allowed a 20% discount to the retailer on the printed price after he gave a 30% discount to the wholesaler. Retailers sell goods to consumers at printed prices, so the wholesaler and retailer each pay 10% sales tax.

Solution:

The price at which the article is sold to the manufacturer

The wholesaler receives a printed price-discount

Wholesaler’s input tax

It refers to the price at which the article is sold by the wholesaler

Retailer’s printed price – discount

The wholesaler’s output tax

Therefore, the wholesaler is liable for VAT

=output tax-input tax

=Rs (9.60-8.40)

=Rs 1.20

In the case of the retailer, the price at which the article is sold

=printed price

=Rs 120

As a result, the retailer’s output tax =10% of Rs 120= Rs 12

The retailer’s input tax = wholesaler’s output tax = Rs 9.60

VAT payable by retailers = output tax – input tax

=Rs (12-9.60)

= Rs 2.40

Therefore, VAT paid by the wholesaler is Rs 1.20 and that paid by the retailer is Rs 2.40.

Also, read How to Calculate VAT Inclusive?

## Exercise

1. In this example, a shopkeeper pays 10 percent sales tax on an article he purchases from a wholesaler for 72 rupees. Consumers are charged a 10% sales tax on articles priced at Rs 90 by the shopkeeper. Use the VAT method of calculating sales tax to answer the following questions:
1. Calculate the shopkeeper’s input tax and output tax.
2. The VAT paid by the shopkeeper to the government can be found here.
3. Calculate the shopkeeper’s profit per cent.
2. An article is purchased for Rs 6200 and sold to a customer for Rs 8500. Find the VAT paid by the shopkeeper if the VAT rate is 8%.
3. 10 phials of a medicine are purchased by a shopkeeper for Rs 560; they pay sales tax at the prescribed rate of 4%. His sales tax is charged on the sales of 6 phials at the prescribed rate of 65 rupees per phial. To calculate the input tax and output tax for the sale of 6 phials, you need to find the shopkeeper’s input tax and output tax. Find out the shopkeeper’s VAT liability.
4. An article is purchased by A for 3600 rupees and sold by B for 4800 rupees. A sells the article to B for Rs 5500, and C buys it from B for Rs 5500. Calculate the VAT levied on A and B if the VAT rate is 10%.
5. An individual buys an article from a shopkeeper for Rs 380 and pays a 10% sales tax. VAT of Rs 3 is paid by the shopkeeper. The shopkeeper purchased the article from the wholesaler at a price inclusive of tax and input tax.
6. An article costs Rs 2400 per article according to a manufacturer’s price list. Manufacturers give wholesalers a 25% discount on their goods. The wholesaler allows retailers a 15% discount on the listed price. At all stages of the sales process, sales tax is charged at 8%. Consumers purchase articles from retailers at the listed price. VATs paid by wholesalers and retailers can be found here.
7. 6% sales tax is charged by a retailer to the buyer on an article. There is a listed price of Rs 450 for the article. What is the amount the retailer paid to the wholesaler if he has to pay VAT of Rs 2.40?
8. There is 4% tax on raw material purchased by a manufacturer for Rs 60000. Tax is 12.5% on the ready stock he sells for Rs 92000. The manufacturer’s VAT payment can be found here.
9. The furniture shop Rohit owns in Delhi is owned by Rohit. Buying a dining table for Rs 12000 and selling it for Rs 15000 is the purchase he makes. In the case of a 10% VAT rate, find Rohit’s VAT payment.
10.  There was a price fix of Rs 250 for an article by a manufacturer. The article is subject to a 12% sales tax. In exchange for 10% profit, a wholesaler sold it to a shopkeeper. Consumers bought the item from the shopkeeper at a 15% profit. Combined, determine how much the consumer paid for the item and how much the wholesaler and retailer paid in VAT.

## What does VAT mean in maths?

The government collects value added tax (VAT) from businesses. The VAT is a purchase tax added to the cost of purchases, except food, which is zero-rated because it is considered a necessity. Governments determine VAT percentages based on the cost.

## How do you calculate VAT maths?

Adding VAT to the original cost will give you the total cost. Ten percent of the amount is obtained by dividing by 10. To calculate the VAT, divide the amount by 2 to get 5%. Once the original cost has been added to the VAT, you can determine the total cost.