Almost every percentage question falls into one of three types. Master these three and you can solve any percentage problem.
Type 1 — What Is X% of Y?
Formula: (X ÷ 100) × Y. Example: what is 15% of 80? 15 ÷ 100 = 0.15. 0.15 × 80 = 12.
Mental shortcut: To find 10%, move the decimal point one place left (80 → 8). For 15%, add 10% + half of 10% = 8 + 4 = 12. For 20%, double the 10% figure.
Type 2 — What Percent Is X of Y?
Formula: (X ÷ Y) × 100. Example: 12 is what percent of 80? (12 ÷ 80) × 100 = 0.15 × 100 = 15%.
Type 3 — X Is Y% of What?
Formula: X ÷ (Y ÷ 100). Example: 12 is 15% of what? 12 ÷ (15 ÷ 100) = 12 ÷ 0.15 = 80.
Percentage Change
Formula: (New − Old) ÷ Old × 100. Example: price goes from £50 to £65. Change = (65 − 50) ÷ 50 × 100 = 30% increase. Negative result = decrease.
Percentage Points vs Percentage
These are different. If a tax rate rises from 20% to 25%: that is a 5 percentage point increase, but a 25% relative increase (5 ÷ 20 × 100 = 25%). Confusing these is one of the most common errors in financial reporting.
Reversing a Percentage Increase
To find original value before a percentage increase: divide final value by (1 + rate/100). Price rose 20% to £120: original = 120 ÷ 1.20 = £100. Never simply apply the percentage to the final price — that gives the wrong answer.
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