UCAT percentage change questions
Percentage change = change ÷ original × 100. Divide by the starting value, never the new one. A rise from 100 to 125 is 25%; a fall from 125 to 100 is 20%. Try two below.
Quantitative Reasoning · Question 1 of 20:00 / 0:43
Membership of the Alder club rises from 100 to 125. What is the percentage increase?
Worked answers
1. Membership of the Alder club rises from 100 to 125. What is the percentage increase?
Answer: C: 25%
- Increase = 125 − 100 = 25.
- Percentage increase = 25 ÷ 100 × 100 = 25%.
2. A shop has revenue of £6000 and profit equal to 25% of revenue. Next month costs rise by 12% and revenue rises by 5%. What is profit as a percentage of the new revenue, to one decimal place?
Answer: C: 20.0%
- Original costs = £6000 × 0.75 = £4500.
- New costs = £4500 × 1.12 = £5040.
- New revenue = £6000 × 1.05 = £6300.
- Margin = (6300 − 5040) ÷ 6300 × 100 = 20.0%.
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Use multipliers
| Change | Multiply by |
|---|---|
| Up 12% | 1.12 |
| Down 15% | 0.85 |
| Up 5% then up 5% | 1.05 × 1.05 = 1.1025 |
Two rises of 5% make 10.25%, not 10%. Chain the multipliers rather than adding percentages.
Back to the original
If £138 is after a 15% rise, the original is 138 ÷ 1.15 = £120. Taking 15% off £138 gives £117.30, the classic wrong answer.
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