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# GCSE Maths | Percentages
- URL: https://www.a-level-maths-tutor.com/gcse-maths-percentages/
- Published: 2026-07-22T11:01:52.000Z
- Updated: 2026-07-22T13:09:04.000Z
- Author: Jaisul Naik
- Tags: GCSE Maths

Percentage change $= \\dfrac{\\text{new} - \\text{old}}{\\text{old}} \\times 100$

**Worked Example**

Original: 60, New: 72

Percentage change $= \\dfrac{72-60}{60} \\times 100 = \\dfrac{12}{60}\\times 100 = 20\\%$ increase

## Question 1

Calculate the percentage change.

**a)** Original: 50, New: 65

**b)** Original: 80, New: 68

**c)** Original: £120, New: £138

**d)** Original: 25g, New: 30g

**e)** Original: 600ml, New: 450ml

**f)** Original: £75, New: £90

**g)** Original: 12cm, New: 15cm

**h)** Original: 250 people, New: 235 people

**i)** Original: 40km, New: 52km

**j)** Original: £950, New: £1,045

Show Answers 

**a)** $+30\\%$

**b)** $-15\\%$

**c)** $+15\\%$

**d)** $+20\\%$

**e)** $-25\\%$

**f)** $+20\\%$

**g)** $+25\\%$

**h)** $-6\\%$

**i)** $+30\\%$

**j)** $+10\\%$

**Worked Example (non-calculator)**

Increase 160 by 12.5%

$100\\% = 160$

$10\\% = 16$

$2.5\\% = 4$

$12.5\\% = 10\\% + 2.5\\% = 16 + 4 = 20$

$160 + 20 = 180$

## Question 2 (Non-Calculator)

Find the new amount after the percentage increase.

**a)** Increase 100 by 10%

**b)** Increase 200 by 15%

**c)** Increase 80 by 25%

**d)** Increase £60 by 50%

**e)** Increase 40 by 5%

**f)** Increase 120 by 12.5%

**g)** Increase 300 by 1%

**h)** Increase 250 by 20%

**i)** Increase 180 by 75%

**j)** Increase 16 by 150%

Show Answers 

**a)** $110$

**b)** $230$

**c)** $100$

**d)** $£90$

**e)** $42$

**f)** $135$

**g)** $303$

**h)** $300$

**i)** $315$

**j)** $40$

**Worked Example (non-calculator)**

Decrease 240 by 17.5%

$100\\% = 240$

$10\\% = 24$

$5\\% = 12$

$2.5\\% = 6$

$17.5\\% = 10\\% + 5\\% + 2.5\\% = 24 + 12 + 6 = 42$

$240 - 42 = 198$

## Question 3 (Non-Calculator)

Find the new amount after the percentage decrease.

**a)** Decrease 100 by 10%

**b)** Decrease 200 by 25%

**c)** Decrease 80 by 50%

**d)** Decrease £60 by 5%

**e)** Decrease 150 by 20%

**f)** Decrease 120 by 75%

**g)** Decrease 400 by 1%

**h)** Decrease 240 by 12.5%

**i)** Decrease 180 by 15%

**j)** Decrease 32 by 150%

Show Answers 

**a)** $90$

**b)** $150$

**c)** $40$

**d)** $£57$

**e)** $120$

**f)** $30$

**g)** $396$

**h)** $210$

**i)** $153$

**j)** $-16$

**Worked Example (calculator)**

Increase 350 by 8%

$350 \\times 1.08 = 378$

## Question 4 (Calculator)

Find the new amount after the percentage increase.

**a)** Increase 134 by 17%

**b)** Increase 278 by 23%

**c)** Increase £85.50 by 12%

**d)** Increase 643 by 8.5%

**e)** Increase 92 by 14.5%

**f)** Increase 1250 by 3.7%

**g)** Increase 87.6 by 21%

**h)** Increase 455 by 16.4%

**i)** Increase £12.99 by 9%

**j)** Increase 782 by 0.5%

Show Answers 

**a)** $156.78$

**b)** $341.94$

**c)** $£95.76$

**d)** $697.66$

**e)** $105.34$

**f)** $1296.25$

**g)** $106.00$

**h)** $529.62$

**i)** $£14.16$

**j)** $785.91$

**Worked Example (calculator)**

Decrease 480 by 22%

$480 \\times 0.78 = 374.40$

## Question 5 (Calculator)

Find the new amount after the percentage decrease.

**a)** Decrease 156 by 18%

**b)** Decrease 289 by 32%

**c)** Decrease £74.80 by 15%

**d)** Decrease 821 by 6.5%

**e)** Decrease 105 by 12.8%

**f)** Decrease 1450 by 4.3%

**g)** Decrease 67.9 by 11%

**h)** Decrease 522 by 17.8%

**i)** Decrease £25.50 by 22%

**j)** Decrease 950 by 1.2%

Show Answers 

**a)** $127.92$

**b)** $196.52$

**c)** $£63.58$

**d)** $767.64$

**e)** $91.56$

**f)** $1387.65$

**g)** $60.43$

**h)** $429.08$

**i)** $£19.89$

**j)** $938.60$

**Worked Example (decrease)**

After a 30% decrease, a chair costs £77\. Find the original price.

$70\\% = £77$

$10\\% = £77 \\div 7 = £11$

$100\\% = £11 \\times 10 = £110$

## Question 6 (Reverse Percentages (Decrease) — Non-Calculator)

Find the original price in each case.

**a)** After a 20% decrease, a jacket costs £64\. What was the original price?

**b)** A bike is sold for £72 after a 10% discount. What was the original price?

**c)** A tablet's value dropped by 30% to £84\. What was the original value?

**d)** A sale reduces a phone's price by 25% to £180\. What was the original price?

**e)** After a 15% reduction, a microwave costs £102\. What was its original price?

**f)** A sofa is sold for £340 after a 15% discount. Find its original price.

Show Answers 

**a)** £80

**b)** £80

**c)** £120

**d)** £240

**e)** £120

**f)** £400

**Worked Example (increase)**

After a 40% increase, a watch costs £98\. Find the original price.

$140\\% = £98$

$10\\% = £98 \\div 14 = £7$

$100\\% = £7 \\times 10 = £70$

## Question 7 (Reverse Percentages (Increase) — Non-Calculator)

Find the original price in each case.

**a)** After a 20% increase, a concert ticket costs £84\. What was the original price?

**b)** A coat was increased by 25% to £75\. What was the price before the increase?

**c)** The price of petrol rose by 10% to £1.65 per litre. What was the original price?

**d)** After a 50% increase, a trampoline costs £150\. What was the original price?

**e)** A laptop's price rose by 30% to £520\. What was its price before the rise?

**f)** A phone plan increased by 25% to £62.50\. What was the price before?

Show Answers 

**a)** £70

**b)** £60

**c)** £1.50

**d)** £100

**e)** £400

**f)** £50

When the percentage isn't a multiple of 10, find 1% instead, then scale up to 100%.

**Worked Example (decrease)**

After a 15% decrease, a laptop costs £425\. Find the original price.

$85\\% = £425$

$1\\% = £425 \\div 85 = £5$

$100\\% = £5 \\times 100 = £500$

## Question 8 (Reverse Percentages (Decrease) — Calculator)

Find the original price in each case.

**a)** A jacket is £68.40 after a 12% discount. What was the original price?

**b)** A fridge is £336.70 after a 15% decrease. What was the full price?

**c)** A tablet dropped 8.5% in value to £293.38\. What was the original value?

**d)** After a 17% decrease, a coat costs £141.27\. What was the price before?

**e)** A gym membership now costs £445.50 after a 10.5% discount. What was the full price?

**f)** A washing machine is £742.32 after a 22% discount. What was the original price?

Show Answers 

**a)** £77.73

**b)** £396.12

**c)** £320.63

**d)** £170.20

**e)** £497.77

**f)** £951.69

**Worked Example (increase)**

After a 9% increase, a subscription costs £272.50\. Find the original price.

$109\\% = £272.50$

$1\\% = £272.50 \\div 109 = £2.50$

$100\\% = £2.50 \\times 100 = £250$

## Question 9 (Reverse Percentages (Increase) - Calculator)

Find the original price in each case.

**a)** A phone rose by 12.5% to £675\. What was the original price?

**b)** A gym membership increased by 15.6% to £580.62\. What was the original price?

**c)** The cost of heating went up 18% to £885.40\. What was it before?

**d)** A sofa price increased by 20.5% to £1,150\. What was its original price?

**e)** A subscription rose by 7.2% to £128.64\. What was it originally?

**f)** A house deposit increased by 25% to £62,500\. What was it before?

Show Answers 

**a)** £600.00

**b)** £502.27

**c)** £750.34

**d)** £954.36

**e)** £120.00

**f)** £50,000.00

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