Reverse Percentages

Sample Reverse Percentages questions

A few of the 40 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 12 marksGrade 3
   Ed's profit on "Good Luck" cards in 2018 was £360. This was a decrease of 20% on his profit in 2017. Work out Ed's profit on "Good Luck" cards in 2017.
   Show the worked solution

   2018 profit (£360) = 80% of 2017 profit. M1

   2017 profit = 360 ÷ 0.8 = £450. A1
2. Question 22 marksGrade 4-5
   Milo buys a sofa. The price including VAT at 20% is £856.8. Work out the price of a sofa before VAT was added.
   Show the worked solution

   The given price represents 120% of the original price, NOT 100% - the original price is what we're finding.

   Write the multiplier: $120\% = 1.2$

What are the common mistakes in Reverse Percentages?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Uses the wrong operation or sign when translating a worded description into an algebraic expression

  Treated the given price of £100.8 as 100% and found 120% of it directly (£120.96), instead of recognising £100.8 already represents 120% of the original - needed to divide by the multiplier 1.2, not multiply by a percentage of the changed amount

• Applies the wrong inverse operation when isolating the unknown (e.g. subtracts instead of adding, or vice versa)

  Multiplied the new price by the multiplier again instead of dividing by it

• Reverses a percentage decrease by adding back the same percentage of the AFTER value, instead of recognising the after value as the reduced percentage of the original and dividing accordingly.

  Adds 20% of £360 (£72) to get £432, instead of recognising £360 is 80% of the original and dividing by 0.8.

Quick answers about Reverse Percentages

How many Reverse Percentages practice questions are there?

There are 40 self-marking GCSE and IGCSE Maths questions on Reverse Percentages, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Extended tier. Each one is marked instantly and has a full worked solution.

Do I need an account to practise Reverse Percentages?

No. You can start practising Reverse Percentages straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.