Sheet № 37 · Foundation + Higher · AQA · Edexcel · OCR
Reverse Percentages
Reverse percentage questions ask you to work backwards — you are given the amount after a percentage change and must find the original amount before the change happened. These questions appear at Foundation and Higher tier on AQA, Edexcel and OCR papers, and they catch out a surprising number of students who try to simply reverse the perc
§Key definitions
Question:
In a sale, a jacket is reduced by 30%. The sale price is £56. What was the original price?
Step 1:
This is a 30% decrease. Multiplier = 1 − 0.30 = 0.70.
Step 2:
The sale price represents 70% of the original.
Step 3:
Original price = £56 ÷ 0.70 = £80
Check:
£80 × 0.70 = £56 ✓
§Formulas to memorise
Original = New value ÷ Multiplier
Original = New value ÷ (1 + r/100)
Original = New value ÷ (1 − r/100)
Identify the percentage change — and whether it is an increase or a decrease.
Calculate the multiplier: — Increase of r% → multiplier = 1 + r/100
Divide — the given (new) value by the multiplier.
State the original value. — 5. Check by applying the percentage change to your answer — you should get back to the given value.
Increase of r% → multiplier = 1 + r/100
Decrease of r% → multiplier = 1 − r/100
Worked example
In a sale, a jacket is reduced by 30%. The sale price is £56. What was the original price?
Step 1: This is a 30% decrease. Multiplier = 1 − 0.30 = 0.70.
⚠ Common mistakes
- ✗Adding or subtracting the percentage of the new value. This is the single most common error. Remember: the percentage was applied to the original, not the new value. You must divide by the multiplier, not add/subtract a percentage of what you have been given.
- ✗Using the wrong multiplier. For a decrease, the multiplier is less than 1 (e.g., 0.70 for a 30% decrease). For an increase, it is greater than 1 (e.g., 1.12 for a 12% increase). Mixing these up reverses the direction.
- ✗Confusing the question type. Not every percentage question is a reverse percentage. If the question gives you the original and asks for the new value, that is a standard percentage increase/decrease. Reverse percentage starts from the result and asks for the original.
- ✗Not checking the answer. Always multiply your original by the multiplier to verify you get back to the number in the question.
✦ Exam tips
- →Identify reverse percentage questions by looking for phrases like "after an increase of ...", "the sale price is ...", "after depreciation the value is ...". These all signal that you have the new value and need the original.
- →Write the multiplier explicitly. On AQA and Edexcel mark schemes, identifying the correct multiplier earns a method mark even if your division is wrong.
- →For VAT questions, if a price includes 20% VAT, the multiplier is 1.20. To find the price before VAT, divide by 1.20. This is a very common exam context.
- →Show your check. While not always required, writing "Check: £80 × 0.70 = £56 ✓" demonstrates confidence and can earn a quality-of-written-communication mark.
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