GCSE Maths, Unit 3, Lesson 5 of 5
Brainlag Plus

Reverse percentages and repeated change

GCSE Maths, Fractions, decimals and percentages, 25 minutes

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Work back to the original amount after a percentage change, take VAT off, combine two changes and compare deals.

Work backwards with the multiplier

After a 20% discount, a price is 80% of the original.

So divide by 0.8, do not add 20% back.

  1. sale price £36 after 20% off
  2. £36 is 80% of the original
  3. original = £36 ÷ 0.8 = £45

Check: 20% of £45 is £9, and £45 − £9 = £36. Adding 20% of £36 gives £43.20, which is wrong, because the 20% was of the original.

Prices with VAT at 20% are 120% of the price without: divide by 1.2.

The rest of this lesson and its 7 practice questions are in Plus.

Screen 1 of 3, free to read.

  • 7 exam-style questions, marked as you go, each with a worked solution
  • The Scientific Calculator beside every question
  • Anything you get wrong is saved to your flashcards