Increasing/Decreasing by a Percentage Textbook Exercise - Corbettmaths - Free Printable

Let's solve Question 1 and Question 2 step by step, which involve increasing or decreasing quantities by a percentage.

We'll use the formula:

> New value = Original value × (1 + percentage change as a decimal)
> For increase: add the percentage
> For decrease: subtract the percentage

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🔷 Question 1: Increase by a Percentage

#### (a) Increase 20 by 50%
- 50% of 20 = $ \frac{50}{100} \times 20 = 10 $
- New value = $ 20 + 10 = 30 $

✔ Answer: 30

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#### (b) Increase 60p by 10%
- 10% of 60p = $ \frac{10}{100} \times 60 = 6 $p
- New value = $ 60 + 6 = 66 $p

✔ Answer: 66p

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#### (c) Increase 12g by 25%
- 25% of 12g = $ \frac{25}{100} \times 12 = 3 $g
- New value = $ 12 + 3 = 15 $g

✔ Answer: 15g

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#### (d) Increase 400 litres by 20%
- 20% of 400 = $ \frac{20}{100} \times 400 = 80 $
- New value = $ 400 + 80 = 480 $ litres

✔ Answer: 480 litres

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#### (e) Increase 32ml by 75%
- 75% of 32 = $ \frac{75}{100} \times 32 = 24 $
- New value = $ 32 + 24 = 56 $ml

✔ Answer: 56ml

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#### (f) Increase 70m by 40%
- 40% of 70 = $ \frac{40}{100} \times 70 = 28 $
- New value = $ 70 + 28 = 98 $m

✔ Answer: 98m

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#### (g) Increase 9000 by 5%
- 5% of 9000 = $ \frac{5}{100} \times 9000 = 450 $
- New value = $ 9000 + 450 = 9450 $

✔ Answer: 9450

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#### (h) Increase £7 by 20%
- 20% of £7 = $ \frac{20}{100} \times 7 = 1.40 $
- New value = $ 7 + 1.40 = £8.40 $

✔ Answer: £8.40

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#### (i) Increase 9kg by 100%
- 100% of 9kg = $ \frac{100}{100} \times 9 = 9 $kg
- New value = $ 9 + 9 = 18 $kg

✔ Answer: 18kg

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🔷 Question 2: Decrease by a Percentage

Use:
> New value = Original value × (1 - percentage change as a decimal)

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#### (a) Decrease 40 by 10%
- 10% of 40 = $ \frac{10}{100} \times 40 = 4 $
- New value = $ 40 - 4 = 36 $

✔ Answer: 36

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#### (b) Decrease 30 hours by 50%
- 50% of 30 = $ \frac{50}{100} \times 30 = 15 $
- New value = $ 30 - 15 = 15 $ hours

✔ Answer: 15 hours

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#### (c) Decrease 8kg by 25%
- 25% of 8 = $ \frac{25}{100} \times 8 = 2 $
- New value = $ 8 - 2 = 6 $kg

✔ Answer: 6kg

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#### (d) Decrease 55cm by 40%
- 40% of 55 = $ \frac{40}{100} \times 55 = 22 $
- New value = $ 55 - 22 = 33 $cm

✔ Answer: 33cm

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#### (e) Decrease 64 by 75%
- 75% of 64 = $ \frac{75}{100} \times 64 = 48 $
- New value = $ 64 - 48 = 16 $

✔ Answer: 16

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#### (f) Decrease £3 by 10%
- 10% of £3 = $ \frac{10}{100} \times 3 = 0.30 $
- New value = $ 3 - 0.30 = £2.70 $

✔ Answer: £2.70

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#### (g) Decrease 1400 by 30%
- 30% of 1400 = $ \frac{30}{100} \times 1400 = 420 $
- New value = $ 1400 - 420 = 980 $

✔ Answer: 980

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#### (h) Decrease 500g by 3%
- 3% of 500 = $ \frac{3}{100} \times 500 = 15 $
- New value = $ 500 - 15 = 485 $g

✔ Answer: 485g

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#### (i) Decrease 6kg by 5%
- 5% of 6 = $ \frac{5}{100} \times 6 = 0.3 $
- New value = $ 6 - 0.3 = 5.7 $kg

✔ Answer: 5.7kg

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✔ Final Answers Summary:

#### Question 1: Increase
| Part | Answer |
|------|--------|
| (a) | 30 |
| (b) | 66p |
| (c) | 15g |
| (d) | 480 litres |
| (e) | 56ml |
| (f) | 98m |
| (g) | 9450 |
| (h) | £8.40 |
| (i) | 18kg |

#### Question 2: Decrease
| Part | Answer |
|------|--------|
| (a) | 36 |
| (b) | 15 hours |
| (c) | 6kg |
| (d) | 33cm |
| (e) | 16 |
| (f) | £2.70 |
| (g) | 980 |
| (h) | 485g |
| (i) | 5.7kg |

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💡 Tip: You can also use the multiplier method:
- To increase by 50% → multiply by $ 1 + 0.5 = 1.5 $
- To decrease by 10% → multiply by $ 1 - 0.1 = 0.9 $

For example:
- (a) $ 20 \times 1.5 = 30 $
- (a) Q2: $ 40 \times 0.9 = 36 $

This is faster for calculations!

Let me know if you'd like these explained in another way! 😊