11+ Percentage Increase and Decrease: Worked Questions
Find new amounts, compare successive percentage changes and recover an original price, with eight explained questions and clear base-value checks.
A percentage change has two parts: the size of the percentage and the amount it applies to. Before calculating, name that starting amount. A reduction of 15% does not mean subtracting £15 unless the original price happens to be £100.
These original questions support preparation for exams taken in 2027. They are not official school papers. Topic coverage and question formats vary: check your target school’s current information. Try the questions on paper before opening each answer.
Find the change, then the new amount
For an increase, calculate the percentage of the original amount and add it. For a decrease, calculate that percentage and subtract it. Start with familiar building blocks: 10% is one tenth, 5% is half of 10%, and 25% is one quarter. Keep money in consistent units.
A £64 item is reduced by 25%. One quarter of £64 is £16, so £16 is the saving. The new price is £64 − £16 = £48. If the question asks how much you save, answer £16; if it asks what you pay, answer £48. Those two correct calculations answer different questions.
For a 15% increase on 260, first find 10% = 26 and 5% = 13. The increase is 39, and the new value is 299. Check that an increase on a positive amount has made it larger. This check will not prove your arithmetic, but it catches an accidental subtraction.
An alternative: the percentage remaining
| Change | New amount as a percentage of the original |
|---|---|
| Increase by 12% | 112% |
| Decrease by 12% | 88% |
| Decrease by 25% | 75% |
You can use these relationships directly: reducing a positive amount by 25% leaves three quarters. The change is one quarter; the new amount is three quarters. Do not confuse a percentage with a number of pounds, centimetres or pupils.
Successive changes use successive bases
A £50 ticket increases by 20%, making £60. It then decreases by 20% of its current price: 20% of £60 is £12, so the final price is £48. The percentages are equal, but the amounts added and removed are different. An equal rise and fall need not return a value to its starting point.
Put each stage on its own line and label the current amount. Do not combine successive percentages by simply subtracting one rate from another. For example, a discount followed by a further discount needs the second discount calculated on the reduced price.
Stretch: work backwards from a sale price
After a 30% reduction, a bag costs £42. This £42 represents 70% of the original price, not 100%. Divide by 7 to find 10% = £6, then multiply by 10 to recover 100% = £60. Check: 30% of £60 is £18 and £60 − £18 = £42.
Adding 30% of £42 would use the wrong base. Reverse questions are a separate step from finding a percentage of a known whole; try them after the forward method feels secure. Do not assume this extension appears in every school’s assessment.
Eight original questions
1. Increase 180 by 15%.
Show answer and explanation
207
10% is 18 and 5% is 9. Add the increase of 27 to 180.
2. Reduce £72 by 25%.
Show answer and explanation
£54
The saving is £18, one quarter of £72. Subtract it from £72.
3. A £90 coat is reduced by 12%. How much money is saved?
Show answer and explanation
£10.80
10% is £9 and 2% is £1.80. The question wants the saving, not the £79.20 sale price.
4. A £45 kit rises in price by 20%, then falls by 10% of the increased price. Find its final price.
Show answer and explanation
£48.60
The increase makes £54. Ten per cent of £54 is £5.40, leaving £48.60.
5. After a 20% reduction, a lamp costs £56. What was its original price?
Show answer and explanation
£70
£56 is 80%. Divide by 8 for 10% = £7, then multiply by 10. Check: £70 less £14 = £56.
6. After a 10% increase, a fee is £66. What was it before the increase?
Show answer and explanation
£60
£66 is 110%. Divide by 11 for 10% = £6, then multiply by 10.
7. A £40 price falls by 25%, then rises by 25% of the sale price. Does it return to £40? Give the final price.
Show answer and explanation
No; £37.50
The reduction makes £30. The rise is £7.50, giving £37.50. The second percentage uses £30.
8. A length of 250 cm increases by 8%. What is the new length?
Show answer and explanation
270 cm
1% is 2.5 cm, so 8% is 20 cm. Add the change to the original length.
Before choosing an answer
- Name the base amount and keep its units.
- Decide whether the question wants the change, the new value or the original value.
- In a reverse question, label the given amount with its actual percentage before calculating.
Review percentages of amounts if the building blocks need practice. Our conversion guide connects percentages with fractions and decimals. Return to the maths hub for related original practice.
Learning context: Department for Education maths programme. Percentage and proportion skills support this work; the guide is not a claim that every question here belongs to one universal exam specification. All examples and keys checked 24 October 2026.
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Choose original practice and use the answer explanations to decide what to work on next. These are not official school papers.
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