Goods and Services Tax (GST) Revision Notes for VCE SSCE General Mathematics

Goods and Services Tax (GST)

What is GST?

The Goods and Services Tax (GST) is a tax of 10% that is added to the price of most goods and services sold in Australia. When you purchase items or use services, GST is typically included in the final price you pay.

GST is an example of a percentage increase. This means the price you pay is the original price plus an additional 10%.

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GST applies to most goods and services in Australia, but some items like basic food, medical services, and educational courses are GST-free. When shopping, always check whether the displayed price includes or excludes GST.

Understanding the GST rate

Since GST is 10%, we can express this as a fraction or decimal:

$10\% = \frac{10}{100} = \frac{1}{10}$

This tells us that finding 10% of an amount is the same as dividing that amount by 10.

Calculating the amount of GST when the cost without GST is known

When you know the price before GST has been added (the original cost), you can calculate how much GST will be charged using this formula:

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Formula for finding GST from original price:

$\text{Amount of GST} = \frac{\text{Cost without GST}}{10}$

This formula works because GST is 10% of the original amount, and finding 10% is the same as dividing by 10.

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Worked Example: Calculating GST on an electricity bill

Question: If the cost of electricity in one quarter is $288.50, how much GST will be added?

Solution:

Use the formula for finding the amount of GST:

$\text{Amount of GST} = \frac{\text{Cost without GST}}{10}$

Substitute $288.50 into the formula:

$\text{Amount of GST} = \frac{288.50}{10} = 28.85$

Answer: The GST is $28.85.

Calculating the total price including GST

When GST needs to be added to a price, you can use two different methods to find the final price.

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Two approaches to adding GST:

There are two equally valid methods for calculating the GST-inclusive price. Method 1 breaks the calculation into steps, while Method 2 uses a single calculation. Choose the method that makes more sense to you!

Method 1: Calculate GST separately then add

Step 1: Calculate 10% of the original price to find the GST amount.

Step 2: Add this GST amount to the original price.

Method 2: Calculate 110% directly

An increase of 10% means the new amount will be 100% (the original) plus 10% (the GST), which equals 110% of the original price.

Step 1: Calculate 110% of the original price.

This gives you the final price in one calculation.

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Worked Example: Calculating a plumber's final bill with GST

Question: The bill for services that a plumber provides is $650. GST needs to be added. What is the amount of the final bill with GST included?

Solution - Method 1:

Find 10% of $650:

$10\% \text{ of } 650 = \frac{10}{100} \times 650 = 65$

Add this to the original amount:

$650 + 65 = 715$

Solution - Method 2:

Calculate 110% of $650:

$110\% \text{ of } 650 = \frac{110}{100} \times 650 = 715$

Answer: The amount of the final bill with GST is $715.

Using the 1.1 multiplier

There is another efficient way to calculate prices with GST. Multiplying by 1.1 is equivalent to finding 110% of the original amount (since $\frac{110}{100} = 1.1$ ).

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Formula for adding GST:

$\text{Cost with GST} = \text{Cost without GST} \times 1.1$

Quick method: To add GST to any price, simply multiply by 1.1.

Calculating the original cost (removing GST)

Sometimes you know the final price including GST, and you need to find what the original price was before GST was added.

We can rearrange our previous formula to find the cost without GST:

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Formula for removing GST:

$\text{Cost without GST} = \frac{\text{Cost with GST}}{1.1}$

Quick method: To remove GST from a price, divide by 1.1.

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Worked Example: Finding the original price of an electric guitar

Question: An electric guitar costs $2299 including GST. What is the price without GST?

Solution:

To find the original cost, divide the GST-inclusive price by 1.1:

$2299 \div 1.1 = 2090$

Answer: The price without GST is $2090.

Calculating the amount of GST when the cost with GST is known

We have learned how to find the GST amount when we know the original price (divide by 10). But what if we only know the final price including GST, and we want to know how much of that price is GST?

There is a formula for this situation as well.

Understanding the formula

Remember that when GST is added:

Original cost + 10% of original cost = Cost with GST
This means 110% of the original cost = Cost with GST

We can write this mathematically:

$\frac{110}{100} \times \text{Cost without GST} = \text{Cost with GST}$

Or equivalently:

$\frac{11}{10} \times \text{Cost without GST} = \text{Cost with GST}$

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Deriving the formula:

If we divide both sides by 11, we get:

$\frac{\text{Cost without GST}}{10} = \frac{\text{Cost with GST}}{11}$

But we also know that:

$\frac{\text{Cost without GST}}{10} = \text{Amount of GST}$

Therefore, we can conclude that:

$\text{Amount of GST} = \frac{\text{Cost with GST}}{11}$

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Formula for finding GST from GST-inclusive price:

$\text{Amount of GST} = \frac{\text{Cost with GST}}{11}$

Quick method: To find the GST amount from a GST-inclusive price, divide by 11.

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Worked Example: Finding GST on a desktop computer

Question: A desktop computer sells for $935, including GST. What is the amount of GST that has been added?

Solution:

Use the formula for finding GST from the GST-inclusive price:

$\text{Amount of GST} = \frac{\text{Cost with GST}}{11}$

Substitute $935 into the formula:

$\text{Amount of GST} = \frac{935}{11} = 85$

Answer: The GST is $85.

Summary of GST formulas

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All Key Formulas for GST Calculations:

What you need to find	What you know	Formula
Amount of GST	Cost without GST	$\text{Amount of GST} = \frac{\text{Cost without GST}}{10}$
Amount of GST	Cost with GST	$\text{Amount of GST} = \frac{\text{Cost with GST}}{11}$
Cost with GST	Cost without GST	$\text{Cost with GST} = \text{Cost without GST} \times 1.1$
Cost without GST	Cost with GST	$\text{Cost without GST} = \frac{\text{Cost with GST}}{1.1}$

Exam tips

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Common pitfalls to avoid:

Always check whether a price includes or excludes GST before doing calculations
Remember to round money answers to the nearest cent (two decimal places) when necessary
Don't confuse the two division rules: divide by 10 for original prices, divide by 11 for GST-inclusive prices

Remember that GST is always 10% in Australia
When adding GST, multiply by 1.1 (or calculate 110%)
When removing GST, divide by 1.1
To find just the GST amount: divide by 10 if you know the original price, or divide by 11 if you know the GST-inclusive price

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Key Points to Remember:

GST is a 10% tax added to the price of most goods and services in Australia
To add GST: Multiply the original price by 1.1, or add 10% to the original price
To remove GST: Divide the GST-inclusive price by 1.1
To find GST amount from original price: Divide by 10
To find GST amount from GST-inclusive price: Divide by 11

Goods and Services Tax (GST) (VCE SSCE General Mathematics): Revision Notes