Percentage Change, Discount and GST

This is the percentage that shows up in real life — the sale at the shopping mall, the GST on your receipt, the interest the bank adds to your savings. Every one of these is a percentage change on a starting amount. The big secret is to be very clear about which amount counts as 100 percent. Get that right and these problems become easy money. Let's go shopping.

Parents: let your child predict before they reveal each step. The blue dotted words are tappable definitions, and the "Method tip" boxes name exactly what a PSLE marker rewards in the working — not just the final number.

By the end you'll be able to find a percentage increase or decrease, work out discount, GST and interest, and find the original amount before a change. Here we go.

Percentage increase and decrease

A percentage increase compares the rise to the original amount. Find the change, then write it as a fraction of the original and multiply by 100. If a plant grows from 20 cm to 25 cm, the increase is 5 cm, and 5 over 20 × 100 = 25 percent.

A percentage decrease works the same way using the fall. The amount you compare against is always the ORIGINAL value, not the new one.

Discount

A discount is a percentage decrease on a price. To find the new price, work out the discount amount and subtract it. A bag costs $60 with 20 percent off. The discount is 20 over 100 × 60 = $12, so the sale price is 60 − 12 = $48.

A faster way: if 20 percent is taken off, you pay 80 percent. So the sale price is 80 over 100 × 60 = $48 in one step. Both routes give the same answer.

GST

GST is a tax added to a price, so it is a percentage increase. To find the price with GST, work out the GST amount and add it. If GST is 9 percent and a meal costs $40, the GST is 9 over 100 × 40 = $3.60, so the total is 40 + 3.60 = $43.60.

The shortcut: with 9 percent GST you pay 109 percent of the price. So 109 over 100 × 40 = $43.60 in one step. The starting price is the 100 percent here.

Simple interest

interest is a percentage the bank adds to money you save. To find one year of interest, take the percentage of the starting amount. If you save $200 at 5 percent interest a year, the interest is 5 over 100 × 200 = $10, so after a year you have 200 + 10 = $210.

Interest is just another percentage increase on the original amount — the same skill in a money setting.

Finding the original amount

This is the trickier type: you are given the amount AFTER a change and must find what it was before. The clue is to decide what percentage the given amount represents. If a price after a 20 percent discount is $48, then $48 is 80 percent of the original.

So 80 percent is $48, which means 1 percent is 48 ÷ 80 = $0.60, and 100 percent is 0.60 × 100 = $60. The original price was $60. Always find what 1 percent is worth, then scale to 100 percent.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. A book price rises from $20 to $24. What is the percentage increase?

   20 percent4 percent24 percent

2. A jacket costs $80 with a 25 percent discount. What is the sale price?

   $60$55$20

3. A meal costs $50 before GST. With 9 percent GST, what is the total?

   $54.50$59.00$50.90

4. $300 is saved at 5 percent interest for one year. What is the interest earned?

   $15$30$5

5. After a 20 percent discount, a watch costs $64. What was the original price?

   $80$84$76.80

6. A shop offers 10 percent off a $90 fan. What is the quickest way to find the sale price?

   Pay 90 percent of $90, which is $81Add 10 percent to $90Pay 10 percent of $90

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