VAT, Discounts, and Sale Prices

VAT (Value Added Tax) is a percentage added to a price. Discounts are percentages subtracted from a price. Knowing how to calculate both is an essential everyday maths skill.

VAT (Value Added Tax)

VAT is a tax added to the cost of goods and services. In many countries it is 20%, but it varies.

Adding VAT

$\text{Price with VAT} = \text{Original price} \times \left(1 + \frac{\text{VAT\%}}{100}\right)$

For 20% VAT: multiply by 1.20

Laptop costs £800 before VAT at 20%

$\text{Price} = 800 \times 1.20 = £960$

Finding the Original Price (Reverse VAT)

If you know the price including VAT, divide by the multiplier:

$\text{Original price} = \frac{\text{Price with VAT}}{1.20}$

A phone costs £180 including 20% VAT. What was the price before VAT?

$\text{Original} = \frac{180}{1.20} = £150$

Discounts and Sale Prices

A discount is a percentage reduction from the original price.

$\text{Sale price} = \text{Original price} \times \left(1 - \frac{\text{discount\%}}{100}\right)$

For a 30% discount: multiply by 0.70

Trainers reduced by 25% from £80

$\text{Sale price} = 80 \times 0.75 = £60$

Calculating the Percentage Discount

If you know the original and sale prices:

$\text{Discount \%} = \frac{\text{amount saved}}{\text{original price}} \times 100$

Was £120, now £90 — find the percentage discount

$\text{Discount} = \frac{120 - 90}{120} \times 100 = \frac{30}{120} \times 100 = 25\%$

Tip

Use the multiplier method (e.g. × 0.80 for a 20% discount) — it is faster than calculating the percentage separately and then subtracting.

Real-World Examples

Real world: buying a laptop online

A laptop is listed at £699 excluding VAT at 20%.

$£699 \times 1.20 = £838.80$

The £838.80 on your receipt includes £139.80 in VAT that the retailer collects and passes to the government. Online shops are required to show whether prices include or exclude VAT.

Real world: Black Friday sale

A coat normally costs £180 but is discounted by 35%.

$£180 \times (1 - 0.35) = £180 \times 0.65 = £117$

Large sales events use percentage discounts to make savings feel more significant. Calculating the multiplier directly gives the sale price in one step.

Real world: restaurant service charge

A restaurant meal costs £64 before a 12.5% service charge is added.

$£64 \times 1.125 = £72$

Service charges work exactly like VAT — they are a percentage added on top of the base price. Checking whether service is already included prevents paying twice.

Practice Problems

A jacket costs £65 before VAT at 20%. What is the price including VAT?

Show answer

£65 × 1.20 = £78

A TV is on sale at 15% off its original price of £400. What is the sale price?

Show answer

£400 × 0.85 = £340

A book was £12 and is now £9. What is the percentage discount?

Show answer

(12−9)/12 × 100 = 3/12 × 100 = 25%