Percentage Applications
Apply percentages to real-life situations including discounts, GST, profit and loss, and percentage change.
Discounts
A discount is an amount subtracted from the original price. To find the sale price, calculate the discount amount then subtract it.
Formula
Discount amount = Percentage ÷ 100 × Original price
Sale price = Original price − Discount amount
Example: A pair of shoes costs $120 and is 25% off. What is the sale price?
Step 1: Discount = 25 ÷ 100 × $120 = $30
Step 2: Sale price = $120 − $30 = $90
GST (Goods and Services Tax)
In Australia, GST is a 10% tax added to the price of most goods and services. Prices shown without GST are called ex-GST prices.
Adding GST
Price with GST = Original price × 1.10
Example: $80 ex-GST → $80 × 1.10 = $88
Removing GST
Ex-GST price = Price including GST ÷ 1.10
Example: $110 incl. GST → $110 ÷ 1.10 = $100
Profit and Loss
Businesses buy items at a cost price and sell them at a selling price. If selling price > cost price, there is a profit. If selling price < cost price, there is a loss.
Profit
Profit = Selling price − Cost price
% Profit = Profit ÷ Cost price × 100
Loss
Loss = Cost price − Selling price
% Loss = Loss ÷ Cost price × 100
Example: A bike bought for $200 is sold for $250. Find the percentage profit.
Profit = $250 − $200 = $50
% Profit = 50 ÷ 200 × 100 = 25%
Percentage Change
Percentage change tells us by how much something has increased or decreased relative to its original value.
% Change = (Change ÷ Original value) × 100
A positive result = increase | A negative result = decrease
Example: A town's population rose from 4000 to 4600. What is the percentage increase?
Change = 4600 − 4000 = 600
% Change = 600 ÷ 4000 × 100 = 15% increase
Key Vocabulary
Discount
A reduction in the original price of an item, usually expressed as a percentage.
GST
Goods and Services Tax — a 10% tax added to most items sold in Australia.
Profit
The amount gained when the selling price is greater than the cost price.
Percentage Change
The increase or decrease of a value expressed as a percentage of the original value.
Worked Examples
A jacket is $180. It is on sale for 30% off. Find the sale price.
Step 1: Discount = 30 ÷ 100 × $180 = $54
Step 2: Sale price = $180 − $54 = $126
Alternatively: Sale price = $180 × 0.70 = $126
A plumber charges $350 ex-GST. How much is the total bill including GST?
Step 1: GST amount = 10% of $350 = $35
Step 2: Total = $350 + $35 = $385
Shortcut: $350 × 1.10 = $385
A phone bought for $600 is sold for $510. Find the percentage loss.
Step 1: Loss = $600 − $510 = $90
Step 2: % Loss = 90 ÷ 600 × 100 = 15%
Knowledge Check
Select the correct answer for each question.
Question 1
A shirt costs $60 and has a 20% discount. What is the sale price?
Question 2
A plumber charges $200 ex-GST. What is the total cost including 10% GST?
Question 3
A skateboard bought for $80 is sold for $100. What is the percentage profit?
Question 4
A class has 25 students. The number increases to 30. What is the percentage increase?
Question 5
A bill is $440 including GST. What was the price before GST?
Key Concepts Summary
- ●Discount amount = (Percentage ÷ 100) × Original price. Sale price = Original − Discount.
- ●GST is 10% in Australia. To add GST, multiply by 1.10. To remove GST, divide by 1.10.
- ●Profit = Selling price − Cost price. % Profit = Profit ÷ Cost price × 100.
- ●Percentage change = (Change ÷ Original) × 100. Positive = increase, negative = decrease.