To work backwards from a price that fell and then rose, undo the last change first. Divide by the fraction of the previous price that remains after each change. A 20% discount followed by a 10% increase leaves 88% of the original price.
The Primary Six Mathematics syllabus includes percentage increase and decrease. The original examples below show how to track the changing whole using simple percentage calculations.
- Label the original, discounted and final prices.
- Use the immediately preceding price as the base for each change.
- Reverse the order of the changes when working backwards.
Worked example | The final price is $132
A shop discounts a bag by 20%, then raises the discounted price by 10%. It now costs $132. Find the original price.
The final price is 110% of the discounted price. Divide $132 by 110 and multiply by 100 to get $120. The discounted price is 80% of the original price. Divide $120 by 80 and multiply by 100 to get $150.
Check by moving forward. Twenty per cent of $150 is $30, leaving $120. Ten per cent of $120 is $12, giving $132. Each percentage used a different price.
Why subtracting ten percentage points gives a different answer
A 20% discount takes away $30 in the example, while the 10% increase adds $12. The net reduction is $18 out of $150, or 12%. Subtracting 10 from 20 would treat both changes as though they were measured from the same original price.
Another way to see it is to start with 100%. The first change leaves 80%. The second adds one tenth of that 80%, which is 8% of the original. The final price is 88% of the original.
Try equal percentage changes
A $200 item rises in price by 25%, then falls by 25% of the higher price. The intermediate price is $250 and the final price is $187.50. The two changes are $50 up and $62.50 down.
Cover the original price and recover it from $187.50. First find the higher price by dividing by 0.75. Then divide by 1.25 to find the original $200. A parent can ask “What was 100% at this step?” before each calculation.
Frequently asked questions
Can I use fractions instead of decimals?
Yes. For example, 80% is four fifths and 110% is eleven tenths.
What does 88% describe?
It is the final price as a share of the original price in the $132 example.
Official information
MOE’s 2021 Primary Mathematics syllabus, October 2025 update, Primary Six Percentage. See SEAB’s published 2026 PSLE Mathematics format (0008) for the paper structure. Checked 9 November 2026.