Taxes on Sale of an Item: In mathematics, the tax calculation is related to taxpayers’ selling price and income. It is a charge imposed by the government on the citizens to collect funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax. We calculate tax on the product by multiplying the tax rate with the product’s net selling price.

What Are Taxes?

Tax is the amount that the people pay to the government for the goods and the services provided. In any tax transaction, a couple of parties are involved first one is a taxpayer and the second, a tax collector. A taxpayer is a person or an organisation who is paying the tax to the government. A tax collector is a government or any middleman collecting the tax on behalf of the government.

The very first known tax transaction was done around \(3000 – 2800\,BC\) in Ancient Egypt. In India, taxes were introduced in the year \(1860\) by Sir James Wilson to meet the government’s losses that were based on the Military Mutiny of the year \(1857\). 

Taxes have usually been around since the beginning of civilisation or history. While the Civil War led to the creation of the first income tax in the U.S., the federal income tax, as you know, was officially enacted in \(1913\). You may have heard terms like income tax, value-added tax, service tax, etc. The formula used to calculate tax on the selling price is given below:

Tax amount \( = ₹\left( {{\rm{S}}{\rm{.P}} \times \frac{{{\rm{Tax}}\,{\rm{rate}}}}{{100}}} \right)\)

Example: Assume the item costs is ₹\(50\), and a sales tax of \(5%\) was charged. What would be the bill amount?

First, find \(5\% \) of \(50\).

Now, add this amount to the cost price, \(₹50 + ₹2.5 = ₹52.5\) The total bill amount, including taxes, would be \(₹52.5\).

When the tax amount and the selling price of the item are given, and you have to calculate the tax rate, then you can use the below-given formula:

\({\rm{Tax}}\,{\rm{rate}} = \frac{{{\rm{Tax}}\,{\rm{amount}}}}{{{\rm{Price}}\,{\rm{before}}\,{\rm{tax}}}} \times 100\% \)

Different Types of Taxes

We have two different types of taxes, and they are direct and indirect taxes. Taxes paid by the citizens directly to the government are known as direct taxes. For example, income tax, corporate tax, etc., are considered direct taxes. Taxes paid by the people but not directly collected by the government are known as indirect taxes. For example, sales tax, entertainment tax, excise duty, etc., are some of the examples of indirect taxes.

Indirect taxes are issued by the people who sell the goods or services. These taxes include shop owners and business people, who further pay the indirect tax to the government. Indirect tax can be passed from one entity to the other.

Types of Direct Taxes

1. Income tax: This is the tax which we pay as per the income tax act of \(1961\). This tax applies to the income you generate for the profits, owning the property, salary, etc.

2. Wealth tax: This tax is applied to the Hindu unified family and business along with the individual.

3. Gift tax: This tax was introduced in the year \(1958\). Accordingly when you receive any presents of any kind you have to pay the tax of \(30\%\).

4. Capital gains tax: You have to pay this tax on the gains you make after selling the investment or the property. We have long term capital gains tax and short term capital gains tax.

5. Securities Transaction Tax: You have to pay this tax when you have invested in share trading or the stock market.

Types of Indirect Taxes

1. Value-added tax (VAT): This tax applies to the items you purchase, like food and essential drugs. This is placed at the stages in the supply chain where the value is added.

2. Sales Tax: This tax is applied when you purchase any product either domestically or be it imported.

3. Service Tax: This is the tax that is applied to the services provided by any companies

4. Goods and Service Tax: This tax was introduced in the year \(2017\). This is applied to the consumption stage. And the GST is applied at every stage of the supply chain wherever consumption is taking place.

5. Customs Duty: This tax is applicable when you purchase the product from a different company and import it to India.

6. Toll Tax: This is the tax applied when you are crossing from the toll between the two cities.

Tax on Marked Price

Sales tax is always calculated on the selling price whenever you purchase something in the shop. It is added to the value of the bill. 

They will calculate the tax rate by using the given formula:

\({\rm{Tax}}\,{\rm{rate}} = \frac{{{\rm{Tax}}\,{\rm{amount}}}}{{{\rm{Price}}\,{\rm{before}}\,{\rm{tax}}}} \times 100\% \)

Income Tax Math Formula

The formula used to calculate tax on the selling price is given below:

Tax amount \( = ₹\left( {{\rm{S}}{\rm{.P}} \times \frac{{{\rm{Tax}}\,{\rm{rate}}}}{{100}}} \right)\)

When the tax amount and the selling price of the item are given, and you have to calculate the tax rate, then you can use the below-given formula:

\({\rm{Tax}}\,{\rm{rate}} = \frac{{{\rm{Tax}}\,{\rm{amount}}}}{{{\rm{Price}}\,{\rm{before}}\,{\rm{tax}}}} \times 100\% \)

Tax Calculator/Sales Tax Formula

The formula for calculating the sales tax on the goods or the service is:

Selling price \( \times \) Sales tax rate

When you want to calculate the total cost of a purchase, the formula is: 

Total sale amount \( = \) Selling price \(+\) Sales tax

Solved Examples: Taxes on Sale of an Item

Q.1. George bought a VCR at the list price of (\{\rm{Rs}}\,18,500\) If the VAT rate was \(8\% \) find the amount he had to pay for purchasing the VCR.
Ans: List price of \({\rm{VCR}} = {\rm{Rs}}\,18500,\,{\rm{VAT}} = 8\% \)
\(\therefore \,{\rm{VAT}} = 8\% \) of \({\rm{Rs}}\,18,500 = {\rm{Rs}}\frac{8}{{100}} \times 18,500 = {\rm{Rs}}\,1480\)
So, the total amount which George had to pay for purchasing the VCR.
\( = {\rm{Rs}}\,18500 + {\rm{Rs}}\,1480 = {\mathop{\rm Rs}\nolimits} \,19980\)

Q 2. The price of a TV set inclusive of VAT is \({\rm{Rs}}\,13,\,530\)  If the rate of VAT is \(10\% \) find its basic price.
Ans: Let the basic price of the TV set be \({\rm{Rs}}\,x\)
Then, VAT at the rate of \({\rm{Rs}}\,x = {\rm{Rs}}\frac{{10}}{{100}} \times x = {\rm{Rs}}\frac{x}{{10}}\)
Thus, the sale price of the TV set \({\rm{Rs}}\,x = \left( {x + \frac{x}{{10}}} \right) = {\rm{Rs}}\frac{{11\,x}}{{10}}\)
It is given that the sale price of the TV set is \({\rm{Rs}}\,13,\,530\)
\(\therefore \,\frac{{11\,x}}{{10}} = 13530 \Rightarrow x\, = \,\frac{{13530 \times 10}}{{11}} = 12300\)
Hence, the basic price of the TV set is \({\rm{Rs}}\,12,\,300\)

Q.3. Samir bought a shirt for \({\rm{Rs}}\,336\) including \(12\% \) VAT and a necktie for \(Rs\,110\) including \(10\% \) VAT. Find the printed price (without VAT) of the shirt and necktie together.
Ans: Let the printed price of the shirt be \({\rm{Rs}}\,x\) and that of necktie be \({\rm{Rs}}\,y\)
VAT on shirt \( = 12\%\) of \({\rm{Rs}}\,x = Rs\frac{{12x}}{{100}} = {\rm{Rs}}\frac{{3x}}{{25}}\)
VAT on neck-tie \( = 10\%\) of \({\rm{Rs}}\,y = {\rm{Rs}}\frac{{10y}}{{100}} = {\rm{Rs}}\frac{v}{{10}}.\)
∴ The selling price of the shirt \( = {\mathop{\rm Rs}\nolimits} \left( {x + \frac{{3x}}{{25}}} \right) = {\mathop{\rm Rs}\nolimits} \frac{{28x}}{{25}}\)
And, selling price of necktie \( = {\mathop{\rm Rs}\nolimits} \left( {y + \frac{v}{{10}}} \right) = {\mathop{\rm Rs}\nolimits} \frac{{11v}}{{10}}\)
But, the selling prices of the shirt and the necktie are \(Rs\,336\) and \(Rs\,110\) respectively.
\(\therefore \frac{{28x}}{{25}} = 336\) and \(\frac{{11y}}{{10}} = 110\)
\( \Rightarrow x = \frac{{336 \times 25}}{{28}}\) and \(y = \frac{{110 \times 10}}{{11}}\)
\( \Rightarrow x = 300\) and \(y = 100)\)
Hence, the total printed price of the shirt and necktie \({\rm{ = Rs}}\,{\rm{(300 + 100) = Rs 400 }}{\rm{.}}\)

Q 4. Reena goes to a shop to buy a radio, costing \({\rm{Rs}}\,2568\) The rate of value-added tax is \(7\% \) She tells the shopkeeper to reduce the price of the radio to such an extent that she has to pay \(Rs\,2568\) inclusive of value-added tax. Find the reduction needed at the price of the radio.
Ans: Let the reduced price, excluding the value-added tax, of the radio be \(Rs\,x\)
Then, VAT \( = 7\%\) and \({\rm{Rs}}\,x = {\rm{Rs}}\frac{{7x}}{{100}}\)
∴ The selling price of the radio \( = {\rm{Rs}}\left( {x + \frac{{7x}}{{100}}} \right) = {\rm{Rs}}\frac{{107x}}{{100}}\)
But, the selling price of the set is \({\rm{Rs}}\,2568\)
\(\therefore \frac{{107x}}{{100}} = 2568 \Rightarrow x = \frac{{2568 \times 100}}{{107}} \Rightarrow x = {\rm{Rs}}2400\)
Hence, the reduction needed at the price of the radio \({\rm{ = {\rm{Rs}}}}\,{\rm{(2568 – 2400) = {\rm{Rs}}\,168}}\)

Q 5. David purchased a pair of shoes for \({\rm{Rs}}\,441\) including value-added tax. Suppose the sales price of the shoes is \({\rm{Rs}}\,420\) Find the rate of value-added tax.
Ans: Let the rate of value-added tax be \(x\% \) Then,
Value-added tax \( = x\%\) of \({\rm{Rs}}\,420 = {\rm{Rs}}\left( {\frac{x}{{100}} \times 420} \right) = {\rm{Rs}}\frac{{21x}}{5}\)
∴ The selling price of shoes \( = {\rm{Rs}}\left( {420 + \frac{{21x}}{5}} \right)\)
But, the selling price of shoes is \({\rm{Rs}}\,\,441\)
\(\therefore 420 + \frac{{21x}}{5} = 441 \Rightarrow \frac{{21x}}{5} = 21 \Rightarrow x = 5\)
Hence, the rate of value-added tax is \(5\% \)

Summary

In the given article, we have discussed taxes on sales of an item, then talked about what are taxes followed by different types of taxes. Then we have provided the information about tax on marked price and formula on income tax. We glanced at the information about the tax calculator/sales tax formula. You can even see the solved examples on taxes on the sale of an item, along with a few FAQs.

Learn the Concepts of Taxation

Frequently Asked Questions (FAQs)

Q 1. How do you find the sales tax in math?
Ans: By using the given formulas and the formula for calculating the sales tax on the goods or the service is:
\({\rm{Selling}}\,{\rm{price}}\,{\rm{ \times }}\,{\rm{Sales}}\,{\rm{tax}}\,{\rm{rate}}\)
When you want to calculate the total cost of a purchase, the formula is: 
\({\rm{Total}}\,{\rm{sale}}\,{\rm{amount}}\, = \,\,{\rm{Selling}}\,{\rm{price  +  Sales}}\,{\rm{tax}}\)

Q.2. How is a tax on an item calculated?
Ans: You have to multiply the cost of an item purchased or the service taken by the sales tax to identify the total amount. The equation is shown as below:
\({\rm{Item}}\,{\rm{or}}\,{\rm{service}}\,{\rm{cost }} \times \,{\rm{Sales}}\,{\rm{tax (in}}\,{\rm{decimal}}\,{\rm{form) = Total}}\,{\rm{Sales}}\,{\rm{Tax}}\)
Add the total sales tax to the item or the service amount to get your total cost.

Q 3. What does sales tax mean in math?
Ans: The sales tax is an amount that is different from the selling price of the item you have purchased. Sales tax is always calculated on the selling price whenever you purchase something in the shop. It is added to the value of the bill.

Q 4. How do you calculate tax on selling price?
Ans: You have to use the formula for calculating the tax on the selling price. The formula used to calculate tax on the selling price is given below:
Tax amount \( = ₹\left( {{\rm{S}}{\rm{.P}} \times \frac{{{\rm{Tax}}\,{\rm{rate}}}}{{100}}} \right)\)
Example: Assume the item costs is \(60\) and a sales tax of \(5%\) was charged. What would be the bill amount?
First, find \(5\% \) of \(60\).
\(\frac{5}{{100}}\,\, \times \,60\, = 3\)
Now, add this amount to the cost price, \(₹60 + ₹3 = ₹{\rm{63 }}\) The total bill amount, including taxes, would be \(₹63\)

Q 5. How do you solve sales tax problems? 
Ans: The sales tax is the difference between the amount of the total bill and the item’s price. You will get the sales tax rate when you divide the sales tax by the item’s price.
Example: \(₹17.68 – ₹17.00 = ₹0.68\)
Now, \((₹0.68) \div \ (₹17.00) = 0.04\)
Hence, the sales tax rate here is \(4\% \)

We hope this detailed article on the taxes on sale of an item helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!