Functional Skills Maths · England

Percentage change, discounts and VAT

Work out price rises, pay increases, sale prices and VAT, find the percentage change between two amounts, and — at Level 2 — work backwards to an original price.

Audience
Adults & apprentices
Levels
Level 1 · Level 2 (reverse percentages)
Worked examples
4
Format
Print (A4/Letter) + answers

Learn

Two ways to increase or decrease by a percentage

The step-by-step method finds the percentage first and then adds or subtracts it. A £650 sofa with 20% off: 10% is £65, so 20% is £130, and the sale price is £650 − £130 = £520. This is the method to use in the non-calculator section, because each step is easy to do on paper.

The multiplier method does it in one go. An increase of 20% means you end up with 120% of the original, so multiply by 1.2. A decrease of 20% leaves 80%, so multiply by 0.8. A 3% pay rise is × 1.03; a 15% discount is × 0.85. With a calculator the multiplier is quicker and there are fewer places to make a slip.

VAT

VAT (value added tax) is added to the price of many goods and services in the UK. The standard rate is 20%, and some things, such as home energy, use a reduced rate of 5%. Questions usually tell you which rate to use. A quote of “£340 plus VAT” at 20% means £340 × 1.2 = £408 to pay. Trade prices are often shown without VAT, while shop prices normally include it — reading which one you have is part of the question.

Finding the percentage change

To find a percentage increase or decrease, work out the change, divide by the original amount, and multiply by 100. If rent rises from £750 to £810, the change is £60, and 60 ÷ 750 = 0.08, which is 8%. Always divide by the original (the “before” value), not the new one.

Reverse percentages (Level 2)

Sometimes you know the price after a change and need the price before it. The trap is to take the percentage off the new price. If a drill costs £87 including 20% VAT, the £87 is 120% of the original, not 100%. Divide by the multiplier: £87 ÷ 1.2 = £72.50. Taking 20% off £87 would give £69.60, which is wrong.

The same idea works for discounts. After 15% off, a kettle costs £34. That £34 is 85% of the original, so the original was £34 ÷ 0.85 = £40. A quick check is to apply the change to your answer and see whether you get back to the figure in the question: £40 × 0.85 = £34.

Level 1 typically covers increasing and decreasing amounts by a percentage, including simple discounts. Level 2 adds reverse percentages, percentage change, VAT calculations and problems with more than one step, such as a discount followed by a further reduction.

Worked example 1

Level 1: A sofa costs £650. It is reduced by 20% in a sale. What is the sale price?

  1. 10% of £650 = £65.
  2. 20% = 2 × £65 = £130.
  3. Sale price = £650 − £130 = £520.

Answer: £520.00

Worked example 2

Level 2: An electrician quotes £340 plus VAT at 20%. What is the total cost?

  1. Adding 20% means multiplying by 1.2.
  2. £340 × 1.2 = £408.
  3. Check: VAT is £68, and £340 + £68 = £408.

Answer: £408.00

Worked example 3

Level 2: A drill costs £87 including VAT at 20%. What was the price before VAT?

  1. £87 is 120% of the price before VAT.
  2. Divide by the multiplier: £87 ÷ 1.2 = £72.50.
  3. Check: £72.50 × 1.2 = £87. The VAT was £14.50.

Answer: £72.50

Worked example 4

Level 2: Monthly rent rises from £750 to £810. What is the percentage increase?

  1. Change = £810 − £750 = £60.
  2. Divide by the original: 60 ÷ 750 = 0.08.
  3. × 100 = 8%.

Answer: 8%

Watch out

Common mistakes

  • Removing VAT by taking 20% off the total. Divide by 1.2 instead, because the total is 120% of the original.
  • Dividing by the new amount when finding a percentage change. Always divide the change by the original.
  • Adding two percentage changes together: 25% off and then a further 10% off is not 35% off, because the second discount applies to the already reduced price.
  • Using 1.2 for a 2% increase. A 2% rise is × 1.02; a 20% rise is × 1.2.

Real life

Where you'll use this at work or home

  • Checking a builder's or mechanic's quote that is given “plus VAT”.
  • Working out a new hourly rate or salary after a pay rise.
  • Comparing sale offers and seeing whether a “further 10% off” is as good as it sounds.
  • Running a small business: working out the VAT element of a receipt, or how much prices have risen since last year.

Try it

Practice sheet

Functional Skills Maths · Level 1

Percentage change, VAT and discounts

NameDate

Show your working. Give money to the nearest penny and include units in every answer.

  1. 1.Mia earns £11.50 an hour and gets a 10% pay rise. What is her new hourly rate?
  2. 2.A coat costs £80 and is reduced by 25%. What is the sale price?
  3. 3.A monthly bus pass costs £56 and goes up by 5%. What is the new price?
  4. 4.A laptop priced at £450 is reduced by 10%. What does it cost now?
  5. 5.A quarterly gas bill of £120 rises by 15%. What is the new bill?
  6. 6.A TV costs £390 with 30% off. How much do you save?
  7. 7.A £1,200 holiday needs a 20% deposit. How much is left to pay after the deposit?
  8. 8.Petrol costs £1.40 a litre and rises by 5%. What is the new price per litre?
  9. 9.Work shoes cost £45 with 20% off. What is the sale price?
  10. 10.A gym membership of £30 a month rises by 2%. What is the new monthly cost?
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Questions

Frequently asked questions

The UK standard rate is 20%, and the question will normally tell you. Some items use the reduced 5% rate, so always read the question.

Because the 20% was calculated on the smaller, pre-VAT price. The total is 120% of that price, so dividing by 1.2 takes you back exactly.

Reverse percentages are generally a Level 2 skill. Level 1 focuses on increasing and decreasing amounts by a given percentage.

Apply your answer to the original amount. If you found an 8% rise from £750, then £750 × 1.08 should give the new figure, £810.

Next steps

Fractions, decimals and percentagesConvert, order, and find fractions and percentages of amounts.Money, interest and budgetingBudgets, simple and compound interest, and income tax.Ratio and proportionSharing in a ratio, recipes, best buys and inverse proportion.All Functional Skills Maths topicsThe full learning path, Level 1 and Level 2.

Last reviewed: 9 October 2026

Editor: Paul Smeaton CMgr FCMI