Taxes

Emma once heard her mother discussing about the payment of income tax.

She was curious to know more about taxes.

taxes introduction

Do you know about taxes?

In this mini-lesson, we will learn about taxes including its definition and types with the help of some solved examples and a few interactive questions for you to test your understanding.

Lesson Plan

What Are Taxes?

The amount paid by the people to the government for goods and services provided is called tax. 

There are two parties involved in any tax transaction. They include a tax payer and a tax collector.

A tax payer is the person or an organization who is paying the tax to the government and a tax collector is the government or any middleman collecting tax on behalf of the government.

You may have heard terms like income tax, value added tax, service tax, etc. The government charges a fee on every item that is sold. This fee is meant to be spent on public welfare and is known as tax. The tax charged is always a percentage of the selling price.

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

Tax amount = \($(S.P. \times \dfrac{Tax\ rate}{100})\)

Let's consider an example.

Let’s say an item costs \($50\) and a sales tax of \(5 \%\) was charged. What would be the bill amount?

Let’s first find \(5 \%\) of \(50.\)

\(\begin{align}{5 \over 100} \times 50 = 2.5 \end{align}\)

Now let’s add this amount to the cost price.

\(\begin{align}$50 + $2.5 = $52.5 \end{align}\)

The total bill amount including taxes would be \($52.5\)

When the tax amount and the selling price (S.P.) of an item are given and we have to calculate the tax rate, then we can use the following formula:

Tax rate = \(\dfrac{Tax\ amount}{Price\ before\ tax}\times 100\%\)

Consider the following example.

You purchase a mobile phone whose price before tax is $200 and the tax paid on it is $20.

a $200 mobile phone

Then, the rate of tax paid on that mobile can be calculated by using the above formula. 

\[Tax\ rate=\dfrac{Tax\ amount}{Price\ before\ tax}\times 100%\]

\[Tax\ rate=\dfrac{$20}{$200}\times 100%\]

\[Tax\ rate=10\% \]

Let’s now try and understand how taxes are levied on a discounted product. 

-  Discount is calculated on the selling price excluding taxes. 
-  The tax is applied on the amount arrived at after subtracting the discount value from the selling price. 

Consider the following scenario.

You have ordered a pizza at a restaurant and it costs \($12.\)

a pizza

The restaurant is offering a discount of \(30 \%\) on all dine-in orders.

Hence, the final amount, assuming the restaurant only charges \(10 \%\) service tax, is calculated in the following way.

First, calculate the discounted price.

\(\begin{align} \text{Discount} & = {30 \over 100} \times 12\\ & = $3.6 \end{align}\)

\(\begin{align} \text{Final Bill Amount} & =$12-$3.6 \\ & =$8.4 \end{align}\)

Remember, the tax is charged on the discounted price. We know that \(10 \% \) service tax was charged on the final amount.

\(\begin{align} {10 \over 100} \times $8.4 = $0.84 \end{align}\)

\(\begin{align} \text{Final Amount} &= $8.4 + $0.84 \\ & = $9.24 \end{align}\)


Different Types of Taxes

There are two types of taxes.

They are direct and indirect taxes.

types of taxes - direct tax and indirect tax

Taxes paid by the citizens directly to the government are direct taxes.

For example, income tax, corporate tax, etc. are categorized as direct taxes.

Taxes paid by the people but not directly collected by the government are indirect taxes.

For example, sales tax, entertainment tax, excise duty, etc. are categorized as indirect taxes.

Indirect taxes are collected by the people who sell goods or services. These include shop owners and businessmen, who then further pay the indirect tax to the government.

Indirect tax can be passed from one entity to another.


Tax on Marked Price

We calculate tax on the marked price when the seller sells an item at the marked price without any discount.

In that case, the marked price and the selling price are the same. Thus, tax is calculated on the marked price.

For example, if the marked price on a chair is $1200 and 8% tax is to be paid to the shopkeeper, then the amount of tax to be paid to the shopkeeper can be calculated as:

8% tax on a chair

Tax amount = \($(M.P. \times \dfrac{Tax\ rate}{100})\)

                    = \($(1200 \times \dfrac{8}{100})\)

                    =  \($(12 \times 8)\)

                    = \($96\)

\(\therefore\) We need to pay $96 as tax on the purchase of the chair of marked price $1200.

Always remember that only when the final selling price is the same as the marked price of the item purchased, we calculate tax on the marked price.

Otherwise, we calculate tax on the net amount that the customer is paying to buy a product or a service.

 
important notes to remember
Important Notes
  1. Tax is always calculated on the final selling price of the item after considering discounts, if available on the item.
  2. There are two major categories of taxes and they are direct tax and indirect tax.
  3. Tax is a real-life application of the percentage concept.
  4. We should always compare the tax rate and not the tax amount, as the prices before tax are different for different products.

Solved Examples

Example 1

 

 

Find the tax paid by Bob for a chair if the selling price of the chair is $7, list price is $10, and the tax rate is 6%?

tax paid on chair - list price is $10 and selling price is $7

Solution

List price = \($10\)

Selling price = \($7\)

Given, tax rate = 6%

We always calculate tax on the selling price. Thus, the tax paid by Bob for the chair is:

Tax amount = \($(S.P. \times \dfrac{Tax\ rate}{100})\)

    = \($(7 \times \dfrac{6}{100})\)

= \($0.42\ \ \ \ \)

\(\therefore\) Bob needs to pay $0.42 tax on the purchase of a chair.
Example 2

 

 

Daniel paid $25 for a T-shirt at a sale, while the price tag was $20.

Find the tax rate in percentage.

$20 for a T-shirt

Solution

Before finding the tax rate, we will find the tax amount.

We know that the price before tax = \($20\)

Final price= \($25\)

Therefore,\[\begin{align}\text{Tax amount}&=\text{Final price - Price before tax } \\&= $25 - $20 \\&= $5 \end{align}\] 
We will calculate the tax rate using the below formula:

Tax rate = \(\dfrac{Tax\ amount}{Price\ before\ tax}\times 100\%\)

= \(\dfrac{5}{20}\times 100\%\)

=\(\dfrac{100}{4}\%\)

=\(25\%\)

\(\therefore\) Tax rate is 25% on the T-shirt.
 
Challenge your math skills
Challenging Question

1. Which brand of bag is charging more tax?

Brand Price after tax Price before tax
Sports k $250 $225
Long run $400 $340
Comfort P $100 $80

Interactive Questions

Here are a few activities for you to practice.

Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 

Let's Summarize

The mini-lesson targeted the fascinating concept of taxes. The math journey around taxes started with what a student already knows and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. 

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.


FAQs on Taxes

1. How to calculate tax on a product?

To calculate tax on a product, we multiply the tax rate by the net selling price of the product.

Tax amount = \($(S.P. \times \dfrac{tax\ rate}{100})\)

2. What are taxes?

The amount paid by the people to the government for goods and services provided is called tax. The amount collected by the government as tax is used for public welfare activities.

3. What is the difference between cost price and selling price?

Cost price is the price at which an article is purchased and selling price is the price at which an article is sold.

4. What is the meaning of marked price?

Marked price is the price set by the shopkeeper on the label of the article. It is set by adding the profit margin to the cost price of the article.

5. What is the formula to calculate the rate of tax on a product?

The formula to calculate the rate of tax is given below:

Tax rate = \(\dfrac{Tax\ amount}{Price\ before\ tax}\times 100\%\)

6. What are the different types of taxes?

There are two types of taxes: direct tax and indirect tax.

7. What is direct tax?

Direct tax is the tax directly paid to the government by the customer. Examples of direct taxes are income tax, corporate tax, wealth tax, etc.
  
More Important Topics
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More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus
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