Percentage Increase and Decrease

Grade 3

Finding a percentage of an amount

The core skill everything else builds on: finding a percentage of a number. Percentage just means "out of 100", so to find, say, 30% of 240 you divide by 100 to get 1%, then multiply by 30.

percentage of amount = (percentage ÷ 100) × amount
EXAMPLE
Find 35% of £420.
1% of £420 = £420 ÷ 100 = £4.20. Then 35% = £4.20 × 35 = £147.

Increasing and decreasing by a percentage

To increase by a percentage, find that percentage of the amount and add it on. To decrease by a percentage, find it and subtract.

EXAMPLE
A coat costs £80. It is reduced by 25%. What is the sale price?
25% of £80 = £80 ÷ 100 × 25 = £20. Sale price = £80 − £20 = £60.

The multiplier method — faster every time

There is a slicker way that GCSE questions reward: the multiplier method. Instead of finding the percentage and then adding or subtracting, you combine both steps into a single multiplication.

For an increase of r%, multiply by (1 + r/100). For a decrease of r%, multiply by (1 − r/100). So +20% → ×1.2; −15% → ×0.85.
EXAMPLE
A phone costs £360. VAT of 20% is added. What is the price including VAT?
Multiplier for +20% is 1.20. Price = £360 × 1.20 = £432.

The multiplier method is especially useful when you need to apply repeated percentage changes — just multiply the multipliers together.

Watch out

A common mistake is to find the percentage of the new amount instead of the original. Always apply the percentage to the value you started with before the change.
Nova
Try this one

A house was valued at £\( V \) in 2018.

Its value increased by 15% in 2019, and then increased by a further 4% in 2020.

In 2021, the value of the house was £218 400.

(a) Show that the value of the house at the start of 2019 was £180 000. [3]

(b) By what percentage did the value increase overall from the start of 2019 to the end of 2021? [2]

Nova's hint:

Part (a) requires reverse compound percentage — undo two successive increases to find the original value.

Ask yourself: 'What combined multiplier represents a 15% increase then a 4% increase, and how do I reverse it?' For part (b), use the overall multiplier directly to find the percentage increase from the original.

Try to Solve it with Nova?