Percentage Change and Reverse Percentages
Percentage Change (Increase / Decrease)
To find the percentage change:
$$\text{Percentage change} = \frac{\text{change}}{\text{original}} \times 100$$
Example: A coat costs £80. In a sale, the price drops to £62. Find the percentage decrease.
$$\text{Change} = 80 - 62 = 18; \quad \text{Percentage decrease} = \frac{18}{80} \times 100 = 22.5%$$
Applying a Percentage Change with a Multiplier
The most efficient method uses a multiplier:
| Change | Multiplier |
|---|---|
| Increase by 20% | $\times 1.20$ |
| Decrease by 15% | $\times 0.85$ |
| Increase by 7.5% | $\times 1.075$ |
| Decrease by 2% | $\times 0.98$ |
Example: Increase £350 by 18%.
$$350 \times 1.18 = £413$$
Compound Percentage Change
Apply the multiplier repeatedly for each time period.
$$\text{Final value} = \text{Original} \times (\text{multiplier})^n$$
Example: £2000 invested at 4% per annum compound interest for 3 years.
$$2000 \times 1.04^3 = 2000 \times 1.124864 = £2249.73 \text{ (to nearest penny)}$$
Depreciation (e.g. car value decreasing 12% per year):
$$\text{Value after 5 years} = P \times 0.88^5$$
Reverse Percentages (Finding the Original Value)
When you know the value after a percentage change and want the original, divide by the multiplier (do NOT add/subtract the percentage from the final value — a common error!).
$$\text{Original} = \frac{\text{final value}}{\text{multiplier}}$$
Example: A TV costs £510 after a 15% reduction. Find the original price.
Multiplier $= 0.85$ (100% − 15%)
$$\text{Original} = \frac{510}{0.85} = £600$$
Example: After a 20% increase, a salary is £30,000. Find the original salary.
Multiplier $= 1.20$
$$\text{Original} = \frac{30{,}000}{1.20} = £25{,}000$$
WJEC Exam Tips
- Always identify the original value — it is what you divide into (not the new value).
- On WJEC Higher papers, reverse percentage and compound interest questions appear frequently.
- Multiplier method is more efficient than breaking into 10% / 1% steps — use it when marks allow a calculator.
- For compound interest, distinguish compound (repeated ×) from simple (add the same amount each year).
- Show the multiplier you are using — it earns M1 even if the final answer is wrong.
AI-generated · claude-opus-4-7 · v3-wjec-maths