 maths > commercial-arithmetics

Introduction to Tax

what you'll learn...

overview

This page introduces the terms bill-price, and tax. It explains that the seller collects the tax on behalf of government on the money transacted which is the sale-price and so the tax is calculated as a percent of the sale-price.

tax percent $=100×$$= 100 \times$ (bill price - sale price) $/$$/$ sale price.

tax

We learned about government and its functions in civics or social science. The government lays roads, provide security, et cetera. For these, the government requires money. The government charges some money on each financial transaction. The money charged on a sale is called tax.

The word "tax" means: money charged by the government on financial transactions.

Tax : Money charged by the government on financial transactions is the tax.

bill-price

A shopkeeper sells a pen for $40$$40$ coins. As a statement of sale, the item and its price is printed on a paper and handed over to the buyer.

The statement is called a "bill".

A shopkeeper sells a pen for $40$$40$ coins. The price is inclusive of tax $2$$2$ coins. The sale price is $40-2=38$$40 - 2 = 38$

A shopkeeper sells a pen for $40$$40$ coins. The price is inclusive of tax $2$$2$ coins. The bill mentions the price as

sale-price $38$$38$ coin + tax $2$$2$ coin = total $40$$40$ coins.

The total price $40$$40$ is called "bill price".

A shopkeeper sells a pen for $40$$40$ coins. The price excludes tax of $2$$2$ coins.

The customer pays $42$$42$ coins which is the bill-price, and the sale price is $40$$40$ coins.

terms

The word "inclusive" means: containing as part of the whole.

The word "exclude" means: outside the given whole.

The word "bill" means: a statement of money that is transacted or handled in a sale.

an example

A shopkeeper sells a pen for $40$$40$ coins. The price excludes tax of $2$$2$ coins.
The sale price is $40$$40$ coins.
Tax is $2$$2$ coins.
Billing price is $42$$42$ coins

The tax is usually given as a percentage. There are two ways the tax percent can be given.
•  the tax is given as percentage on the sale-price $\frac{2}{40}×100$$\frac{2}{40} \times 100$ percent.
•  the tax is given as percentage on the bill-total $\frac{2}{42}×100$$\frac{2}{42} \times 100$ percent.

The tax is specified as a percentage of the sale price.

Note that government takes a tax on the sale as a percent.

For example: Sale price is $40$$40$ and tax percent is $5%$. The tax is $2$$2$ coins. The bill price is $42$$42$.

If the tax is calculated on the bill price, then the tax is also taxed. Tax on tax is avoided by taxing the sale-price only.

percent

Tax Percent : The tax as a percent of the sale-price is the tax percentage.
tax percent $=100×$$= 100 \times$ (bill price - sale price) $/$$/$ sale price.

examples

A shopkeeper sells a pen for $44$$44$ coins. The price includes $10%$ tax.
What is the sale-price of the pen?

A shopkeeper sells a pen for $44$$44$ coins. The price includes $10%$ tax.

bill-price = $44$$44$ coins

bill price includes sale price $100%$ and tax $10%$. That is bill-price $110%$ is $44$$44$ coins

$110%$ bill-price $=44$$= 44$ coins
$100%$ sale- price is $=44×100/110$$= 44 \times 100 / 110$ $=40$$= 40$

A shopkeeper sells a pen for $44$$44$ coins. The price excludes $10%$ tax.

What is the sale price?

A shopkeeper sells a pen for $44$$44$ coins. The price excludes $10%$ tax.

sale-price is the given = $44$$44$ coins

the tax on the sale price is $10%$ = $44×10/100=4.4$$44 \times 10 / 100 = 4.4$ coins.

bill price includes sale price and tax . That is bill-price $=44+4.4=48.4$$= 44 + 4.4 = 48.4$ coins.

summary

Price Inclusive of Tax : The marked price includes the tax and so it is the bill price.
marked price = billed price = sale price + tax

Price with Tax Extra : The marked price does not include the tax and so it is the sale price.
marked price = sale-price
billed price = marked price + tax

Outline