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 7 of 8 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Percentage Problems
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
Practice questions for Percentage Problems
What is the multiplier for a 30% increase?
Work out 20% of 60.
Quick recall flashcards
What is the formula for simple interest?
I = PRT/100
where P = Principal, R = Rate (%), T = Time (years)
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