Example 1 · level 1 — a gentle start
A price of £360 is decreased by 50%. What is the new price?
- 180
- 540
- 181
- 310
Answer: 180 — 50% of 360 is 180, so the new price is 180.
11+ percentage increase, decrease and change questions
Percentage increase, decrease and change comes up in the maths paper of every major 11+ format. Here is what the questions look like, the method that works under time pressure, and five worked examples with the full reasoning, from a gentle start to a hard paper.
Maths · examined by GL and CEM · 5 worked examples
What your child needs to know
- Find 10% first by dividing by 10. From there you can build any percentage.
- An INCREASE adds the change on; a DECREASE takes it away. Decide which before you calculate.
Where marks get lost: Careful with reverse questions: if £100 is AFTER a 25% rise, the £100 is 125% of the old price — so divide by 1.25.
Worked examples
Every question below is generated by the same engine your child practises on, and every answer is derived by our checker rather than written by hand — which is why we can put them on a public page at all.
Example 2 · level 2 — typical of early practice
A price of £500 is decreased by 25%. What is the new price?
- 625
- 375
- 125
- 475
Answer: 375 — 25% of 500 is 125, so the new price is 375.
Example 3 · level 3 — standard paper difficulty
A price of £280 is increased by 15%. What is the new price?
- 238
- 42
- 322
- 295
Answer: 322 — 15% of 280 is 42, so the new price is 322.
Example 4 · level 4 — a harder paper
After a 30% increase, a price is £1352. What was it before?
- 1757.6
- 946.4
- 1322
- 1040
Answer: 1040 — The new price is 130% of the old one, so divide by 1.3.
Example 5 · level 5 — the level that separates candidates
A price changes from £2200 to £1936. What is the percentage change?
- 264%
- -14%
- -12%
- 12%
Answer: -12% — Change ÷ original × 100 = (1936 − 2200) ÷ 2200 × 100.
How to practise this at home
- Work in short, frequent sessions. Ten minutes daily beats an hour at the weekend, because the recall gap is what builds memory.
- Insist on written working, even for questions your child can do in their head — under exam pressure the method is what survives.
- When an answer is wrong, ask them to explain their reasoning before you correct it. The error is almost always in one step, not the whole approach.
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