Key Terms
- VAT: Value Added Tax — usually 20% added to the pre-tax price
- Simple interest: Interest calculated only on the original amount each period
- Commission: A percentage of sales earned as pay
- Percentage change: (new − old) ÷ old × 100%
- Reverse percentage: Finding the original value before a percentage was applied
- Multiplier: The decimal used to apply a percentage change in one step
Must-Know Facts
- 20% VAT: multiply by 1.2; remove VAT: divide by 1.2
- 20% off then 10% off ≠ 30% off (it is actually 28% off: 0.8 × 0.9 = 0.72)
- Simple interest formula: I = PRT ÷ 100 (P = principal, R = rate, T = time)
- Reverse %: if price after 20% VAT is £84, original = £84 ÷ 1.2 = £70
- Percentage change = (change ÷ original) × 100%
- Profit % = (profit ÷ cost price) × 100%
Key Formulas
- Simple interest: I = PRT ÷ 100
- % change: (new − old) ÷ old × 100%
- Increase by r%: × (1 + r/100)
- Decrease by r%: × (1 − r/100)
- Reverse %: known value ÷ multiplier
- Commission: sales × rate ÷ 100
Common Mistakes
- % change denominator: Always divide by the ORIGINAL value, not the new value
- Reverse percentage: If after 20% increase = £120, then original is 120 ÷ 1.2 = £100, NOT 120 − 20% of 120
- Simple vs compound interest: Simple uses flat rate each year; compound recalculates on the new total
- VAT problems: To find pre-VAT price, divide by 1.2 (not subtract 20% of given price)
- Percentage point vs percentage change: Going from 40% to 50% is 10 percentage points but a 25% increase
This topic summary covers Knowledge Organiser: Percentage Problems within Percentage Problems for GCSE Mathematics. Revise Percentage Problems in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 8 of 8 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Percentage Problems
What is the multiplier for a 30% increase?
Work out 20% of 60.
Quick recall flashcards
A £60 item has 25% off. What do you pay?
Method 1: Discount = £60 × 0.25 = £15, Pay = £60 - £15 = £45
Method 2: Pay = £60 × 0.75 = £45
Answer: £45
What is the formula for simple interest?
I = PRT/100
where P = Principal, R = Rate (%), T = Time (years)