Percentage change and growth

Numerical reasoning practice > Percentage change and growth

This is where most marks are lost. The trap is almost always the same: the largest absolute increase and the largest percentage increase are different rows, and the question asks for the one you did not calculate.

1. The one formula you need

Percentage change is always:

(new − old) ÷ old × 100

The part people get wrong is the denominator. It is always the starting value, never the new one and never the total. If revenue goes from 500 to 690, the denominator is 500.

2. The trap: absolute versus percentage

Consider two products. One grows from 2,000 to 3,080. The other grows from 600 to 948.

• The first grew by 1,080 — much the larger increase
• The second grew by 348 — much the smaller increase
• But 1,080 ÷ 2,000 = 54%, and 348 ÷ 600 = 58%

The second product grew faster. A question asking "which grew the most" is ambiguous and will not be asked; a question asking "which had the highest percentage growth" is asking you to notice this.

Whenever a question contains the word "percentage", check every row. The row with the biggest number on the page is usually a distractor.

3. Worked example: highest percentage growth

The table below shows how revenue changed for each product.

Product C 2,000 → 3,080
Product D 600 → 948
Product B 1,400 → 1,554
Product A 500 → 690
(2022 and 2024, unit: £000s)

Which product had the highest percentage growth in revenue from 2022 to 2024?

How to work it

• C: 1,080 / 2,000 = 54%
• D: 348 / 600 = 58%
• B: 154 / 1,400 = 11%
• A: 190 / 500 = 38%

The answer is Product D at 58%, even though Product C added three times as much revenue.

A useful shortcut: you do not need exact percentages. D is "a bit more than half again"; C is "about half again". That is enough to separate them.

4. Index numbers

An index sets one year to 100 and expresses the others relative to it. If 2020 = 100 and 2024 = 130, revenue grew 30% over that period.

• An index of 130 means 30% above the base, not 130% above
• Two series with the same index can have completely different absolute values — an index hides scale deliberately
• To compare across series, you need the base value; if it is not given, the question can only be about relative change

5. Percentage points versus per cent

If a share rises from 20% to 25%, that is a rise of 5 percentage points and also a rise of 25 per cent (5 ÷ 20). Both are correct answers to different questions.

Test writers use this deliberately. Read which of the two is being asked for, and note that "percentage point" will be written out in full when it is meant.