Repeated percentage change | Year 10

01 / LEARN

The idea, step by step

Use the new base each time

A 20% discount followed by a 10% discount uses factor $0.8 \times 0.9 = 0.72$ . The second discount acts on the already reduced amount.

The combined discount is 28%, not 30%. Write every factor before evaluating to avoid adding percentages that use different bases.

Reversing a factor

To reverse multiplication by $b$ , divide by $b$ . A 20% decrease uses $0.8$ ; reversing it uses $1 / 0.8 = 1.25$ , so it needs a 25% increase.

An equal percentage increase and decrease do not cancel. Their order does not affect the product when there are no fixed fees or extra transactions, but their changing bases still matter.

A common trap

Add signed percentages even when the base changes.

Instead: Use multipliers for changes to the current amount. Add percentages only when the same fixed base is explicitly used.

02 / WORKED EXAMPLES

See the thinking

Example 1

Two discounts

A 250-dollar item has a 20% discount followed by another 10% discount. Find the final price and overall discount.

$250 (0.8) (0.9) = 180$ .
The retained fraction is $0.72$ , giving an overall 28% discount.

180 dollars; 28% discount.

Example 2

Up then down

An amount rises by 10% then falls by 10%. Find its net percentage change.

The combined factor is $1.1 \times 0.9 = 0.99$ .
It retains 99%, so the net change is a 1% decrease.

1% decrease.

Check your understanding

What increase reverses a 25% decrease?

Show answer

$33 \frac{1}{3} %$

$1 / 0.75 = 4 / 3$ , which is one third above 1.

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

A 400-dollar price rises by 5%, then falls by 5%. Find the final price.
2 marks
Combine increases of 10% and 20%.
2 marks
Combine decreases of 10% and 30%.
2 marks
A final price is 216 dollars after a 10% discount. Find the original price.
2 marks
What percentage increase reverses a 40% decrease?
3 marks
An 800-dollar amount rises 20%, falls 25%, then rises 10%. Find the result and net change.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

A 400-dollar price rises by 5%, then falls by 5%. Find the final price.
2 marks
$400 (1.05) (0.95) = 399$ .
399 dollars
Combine increases of 10% and 20%.
2 marks
$1.1 \times 1.2 = 1.32$ .
32% increase
Combine decreases of 10% and 30%.
2 marks
$0.9 \times 0.7 = 0.63$ .
37% decrease
A final price is 216 dollars after a 10% discount. Find the original price.
2 marks
$216 / 0.9 = 240$ .
240 dollars
What percentage increase reverses a 40% decrease?
3 marks
The reverse factor $1 / 0.6 = 5 / 3$ exceeds 1 by $2 / 3$ .
$66 \frac{2}{3} %$
An 800-dollar amount rises 20%, falls 25%, then rises 10%. Find the result and net change.
3 marks
$800 (1.2) (0.75) (1.1) = 792$ ; the combined factor is $0.99$ .
792 dollars; 1% decrease.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Simple versus compound growth; compound interest; depreciation; repeated percentage change; savings/loan scenarios with supplied models; changing assumptions and checking results; spreadsheets/digital models.

Official curriculum source ↗

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