Knowledge Organiser: Reverse Percentages
Part of Reverse Percentages · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Reverse Percentages within Reverse Percentages for GCSE Mathematics. Revise Reverse Percentages in Ratio & Proportion for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 6 of 6 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 6 of 6
Practice
12 questions
Recall
22 flashcards
Knowledge Organiser: Reverse Percentages
Key Terms
- Reverse percentage: Finding the original value before a percentage change was applied
- Multiplier: The decimal that was applied to get the final amount
- Original amount: The value before the percentage change — what we are finding
- VAT: Value Added Tax, added at 20% — final price is 120% of pre-VAT price
Must-Know Facts
- After a 20% decrease: the final amount is 80% of the original (multiplier = 0.80)
- After a 15% increase: the final amount is 115% of the original (multiplier = 1.15)
- Original = final amount ÷ multiplier
- Never find a percentage of the final amount — that gives the wrong answer
- Always check by multiplying your original by the multiplier to get the final amount back
Key Formulas
- Original = final ÷ multiplier
- For a decrease of n%: multiplier = 1 - (n ÷ 100)
- For an increase of n%: multiplier = 1 + (n ÷ 100)
- Check: original × multiplier = final amount
Common Mistakes
- Subtracting/adding the % from the given value: If £120 is after a 20% increase, do NOT do £120 − 20% of £120 — divide by 1.2
- Wrong multiplier: For a 20% increase, divide by 1.2 (not 0.8); for a 20% decrease, divide by 0.8 (not 1.2)
- Identifying the direction: Read carefully — is the given value after an increase or decrease?
- Not checking: Multiply your answer by the multiplier to verify it gives the stated final amount
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Practice Questions for Reverse Percentages
A price after a 20% increase is £120. Which calculation finds the ORIGINAL price?
A TV costs £360 after a 10% increase. A student says: 'The original price was £360 - 10% = £360 - £36 = £324.' Explain the error in the student's method. What is the correct original price?
Quick Recall Flashcards
12 questions on Reverse Percentages — practise free
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