Percentages Made Easy
All you need to handle percentage questions fast: increase/decrease multipliers, reverse percentages, percentage points vs percentages, and common exam-style traps.
1) Core Multipliers (Fastest Method)
- Increase by x%: multiply by
(1 + x/100) - Decrease by x%: multiply by
(1 − x/100)
Examples
- Increase £240 by 12% →
240 × 1.12 = £268.80 - Decrease £75 by 20% →
75 × 0.80 = £60.00
2) Successive Changes ≠ Add the Percents
Two percentage changes multiply, they don’t add.
Up 10% then down 10%: Price × 1.10 × 0.90 = Price × 0.99 → net 1% decrease.
3) Percentage Points vs Percentages
Going from 3% to 5% is a rise of 2 percentage points (pp), but a 66.7% increase (because (5−3)/3 = 0.667).
- Use pp when comparing rates (e.g., interest or unemployment).
- Use % change when comparing sizes (e.g., revenue).
4) Finding the Percentage Change
% change = (new − old) ÷ old × 100
- From 120 to 150 →
(150−120)/120 × 100 = 25% - From 150 to 120 →
(120−150)/150 × 100 = −20%
5) Reverse Percentages (Work Backwards)
When a price after a percentage change is known, divide by the multiplier.
- After a 20% increase the price is £180 → original =
180 ÷ 1.20 = £150 - After a 15% discount the price is £255 → original =
255 ÷ 0.85 = £300
6) Common Exam-Style Questions
| Question | Method | Answer |
|---|---|---|
| A jacket is £60 after a 25% discount. What was the original price? | Reverse: divide by 0.75 | £80.00 |
| Population rises 8% one year then 5% the next. Overall increase? | Multiply: 1.08 × 1.05 − 1 | 13.4% |
| Tax rate goes from 17% to 20%. Increase in percentage points? | Difference in rates | 3 pp |
| VAT at 20% is included in a £96 price. What’s the net price? | Remove VAT: divide by 1.20 | £80.00 |
| A savings account quotes 4% AER. What’s the monthly rate (approx)? | \( (1+0.04)^{1/12}-1 \) | ≈ 0.327% |
7) Percentages in Finance (Quick Links)
8) Quick Reference
| Task | Use |
|---|---|
| Increase by x% | Multiply by 1 + x/100 |
| Decrease by x% | Multiply by 1 − x/100 |
| Find % change | (new−old)/old × 100 |
| Reverse % increase | Divide by 1 + x/100 |
| Reverse % decrease | Divide by 1 − x/100 |
| Percentage points | Difference between two rates (e.g., 3%→5% = 2 pp) |