Percentage change and reverse percentages
Percentage increase and decrease using a multiplier
The most efficient approach: express the percentage change as a decimal multiplier.
- Increase of p%: multiply by (1 + p/100). e.g. +30% → × 1.30.
- Decrease of p%: multiply by (1 − p/100). e.g. −15% → × 0.85.
New value = original × multiplier. Percentage change = (change ÷ original) × 100.
Reverse percentages (finding the original)
When you know the value AFTER a percentage change, divide by the multiplier.
Original = new value ÷ multiplier.
Example: After a 20% increase, a price is £480. Original = £480 ÷ 1.20 = £400.
The classic Edexcel mistake: students subtract 20% from £480 to get £384. This is wrong because 20% of £480 ≠ 20% of £400 (the original).
VAT problems (Edexcel functional)
UK VAT is 20%. A price including VAT is the original × 1.20. To find the price excluding VAT: divide by 1.20.
Example: A laptop costs £960 including VAT. Price before VAT = £960 ÷ 1.20 = £800.
Percentage profit and loss
Percentage profit = (profit ÷ cost price) × 100. Percentage loss = (loss ÷ cost price) × 100.
Always use the original/cost price as the denominator.
Combined percentage changes
Applying two successive percentage changes is NOT the same as adding them. Example: +10% then −10% → multiplier = 1.10 × 0.90 = 0.99 → net 1% decrease.
Edexcel exam style
Edexcel Papers 2/3 embed percentages in realistic contexts: salary negotiations, sale prices, VAT, population growth, depreciation. The key skill is identifying the original (base) value correctly before applying the multiplier.
⚠Common mistakes
- Reverse percentages: never subtract/add the percentage from/to the new value.
- Wrong denominator in % change: always divide by the ORIGINAL, not the new value.
- Forgetting to multiply by 100 at the end of a percentage calculation.
- Combined changes: 10% + 10% ≠ 20%; always multiply the multipliers.
AI-generated · claude-opus-4-7 · v3-edexcel-maths