Percentages in Real Life (Discounts and Tax)

Percentages are everywhere

The word percent means "out of 100," so 25% means 25 out of 100, or the fraction 25/100, or the decimal 0.25. Once you can switch between those forms, percentages become a powerful everyday tool. You see them on price tags, restaurant bills, bank statements, and news headlines. This lesson is all about using them in real life — especially discounts and tax.

If you want to revisit the basics of converting between fractions, decimals and percentages, Percentages Made Easy is a helpful companion to this lesson.

Finding a percentage of an amount

The core skill is finding a percentage of something. Turn the percent into a decimal and multiply.

$$ 30\% \text{ of } £80 \;=\; 0.30 \times 80 \;=\; £24 $$

A few mental shortcuts make this quick:

• 10% — divide by 10 (10% of £80 = £8).
• 1% — divide by 100 (1% of £80 = £0.80).
• 5% — half of 10% (5% of £80 = £4).
• 25% — a quarter, so divide by 4 (25% of £80 = £20).

Build any percentage from these. For example, 35% of £80 = 10% + 10% + 10% + 5% = £8 + £8 + £8 + £4 = £28.

Discounts: taking money off

A discount is a percentage subtracted from the price. There are two ways to do it.

Method 1 — find and subtract. A £40 jacket has 25% off.

• Discount = 25% of £40 = 0.25 × 40 = £10.
• Sale price = £40 − £10 = £30.

Method 2 — the multiplier (faster). If you take 25% off, you keep 75%. So multiply by 0.75 in one step:

$$ £40 \times 0.75 = £30 $$

The multiplier is the percentage you keep written as a decimal. Take off 30% → keep 70% → ×0.70. Take off 15% → keep 85% → ×0.85.

Tax and tips: adding money on

Tax (such as sales tax or VAT) and tips are percentages added on top of the price.

Worked example — sales tax. A gadget costs £50 before 20% sales tax.

• Tax = 20% of £50 = £10.
• Final price = £50 + £10 = £60.

The multiplier for adding 20% is 1.20 (you have 100% of the price plus 20% more): £50 × 1.20 = £60.

Worked example — a tip. A restaurant bill is £35 and you leave a 15% tip.

• Tip = 10% (£3.50) + 5% (£1.75) = £5.25.
• Total = £35 + £5.25 = £40.25.

A table of common multipliers

This table shows why the multiplier method is so handy. The same idea covers both discounts and tax.

Change	Keep / Add	Multiplier	Example on £200
10% off	keep 90%	× 0.90	£180
20% off	keep 80%	× 0.80	£160
25% off	keep 75%	× 0.75	£150
add 5% tax	100% + 5%	× 1.05	£210
add 20% tax	100% + 20%	× 1.20	£240

Discount and tax together

In the real world you often do both. A coat costs £80, has 25% off, and then 20% tax is added to the reduced price.

1. Apply the discount: £80 × 0.75 = £60.
2. Add the tax: £60 × 1.20 = £72.

So you pay £72. Shops apply the discount first, then tax the lower amount — which is better for you than the other way round would feel, though the maths gives the same final figure either way: 80 × 0.75 × 1.20 = 80 × 1.20 × 0.75 = £72.

Percentage increase and decrease

When a price changes, you can describe the change as a percentage of the original amount.

$$ \text{Percentage change} = \frac{\text{change}}{\text{original}} \times 100 $$

Worked example — increase. A phone's price rises from £200 to £250.

• Change = £250 − £200 = £50.
• Percentage increase = (50 ÷ 200) × 100 = 25%.

Worked example — decrease. A bike falls from £300 to £210.

• Change = £300 − £210 = £90.
• Percentage decrease = (90 ÷ 300) × 100 = 30%.

Always divide by the original value, not the new one — that is the most common mistake.

Reversing a percentage change

Sometimes you know the price after a change and need the original. This is trickier, because you must divide by the multiplier instead of multiplying.

Worked example — finding the original price. A coat is £60 in a sale after 25% off. What was the original price?

The sale price is 75% of the original, so we used the multiplier 0.75. To undo it, divide:

$$ \text{original} = £60 \div 0.75 = £80 $$

Check forward: £80 × 0.75 = £60. ✓ A common error is to add 25% to £60, which gives £75 — wrong, because the 25% was taken off the larger original, not the smaller sale price.

The same trick reverses tax. If a price is £72 including 20% tax, the pre-tax price is £72 ÷ 1.20 = £60, because the £72 is 120% of the original.

Practice activity

Try these with a pencil, then check your answers.

1. Find 15% of £60.
2. A £25 book has 40% off. What is the sale price?
3. A meal costs £48 plus a 12.5% service charge. What is the total?
4. A jacket costs £90 with 30% off, then 20% tax added. What is the final price?
5. A laptop's price drops from £500 to £400. What is the percentage decrease?

Answers: 1) £9 2) £15 (£25 × 0.60) 3) £54 (charge £6) 4) £90 × 0.70 × 1.20 = £75.60 5) (100 ÷ 500) × 100 = 20%.

Why this matters

Percentages turn confusing money decisions into quick comparisons. Knowing how discounts and tax work means you can check a till receipt, judge whether a "50% off" sale is really the bargain it claims, leave a fair tip, and understand interest on savings and loans. The multiplier trick — multiply by 0.80 to take off 20%, by 1.20 to add 20% — is the single most useful percentage skill an adult can have. Practise it until it is automatic, and you will never be caught out at the checkout again.