Percentage Change - Worksheets, Questions and Revision

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GCSE · Number

3.8 Percentage Change

EDEXCEL 1MA1 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Revision notes: Percentage Change

Percentage change measures how much a quantity has increased or decreased, given as a percentage of the original value. It differs from finding a percentage of an amount: percentage change always compares the change to the ORIGINAL value, using the formula (change / original) x 100.

Work out the change: change = new value - original value.
Divide the change by the ORIGINAL value, not the new value.
Multiply by 100 to convert to a percentage.
State whether it is a percentage increase or a percentage decrease, matching the direction of the change.

Worked example. A car was bought for 12000 pounds and sold for 9000 pounds. Work out the percentage change in its value.

Change = 9000 - 12000 = -3000 (a decrease of 3000 pounds).
Percentage change = (change / original) x 100 = (3000 / 12000) x 100.
3000 / 12000 = 0.25; 0.25 x 100 = 25.

Answer: A 25% decrease.

A quantity increases from 40 to 52. Work out the percentage increase.

(Total for Question 1 is 2 marks)

A quantity decreases from 90 to 72. Work out the percentage decrease.

(Total for Question 2 is 2 marks)

Last month a magazine cost 2 pounds. This month it costs 2.50 pounds. Work out the percentage increase in the price of the magazine.

(Total for Question 3 is 3 marks)

A shop's weekly sales fall from 400 units to 340 units. Work out the percentage decrease in weekly sales.

(Total for Question 4 is 3 marks)

Deepak buys a guitar for 80 pounds. He sells it for 92 pounds. Work out Deepak's percentage profit.

(Total for Question 5 is 3 marks)

Farah buys a painting for 250 pounds. She later sells it for 210 pounds. Work out Farah's percentage loss.

(Total for Question 6 is 3 marks)

Last year a gym membership cost 420 pounds. This year it costs 462 pounds. Work out the percentage increase in the cost of the membership.

(Total for Question 7 is 3 marks)

Last year Chidi paid 1380 pounds for his car insurance. This year he pays 1195 pounds. Work out the percentage decrease in his car insurance. Give your answer correct to 1 decimal place.

(Total for Question 8 is 3 marks)

In 2010 the population of a town was 84 600. In 2020 the population was 91 250. Work out the percentage increase in the population. Give your answer correct to 1 decimal place.

(Total for Question 9 is 3 marks)

A company sold 24 800 tablet computers in one year and 23 150 tablet computers the next year. Work out the percentage decrease in the number sold. Give your answer correct to 3 significant figures.

(Total for Question 10 is 3 marks)

Olamide buys a car for 9200 pounds. She sells it for 7820 pounds. Work out Olamide's percentage loss.

(Total for Question 11 is 3 marks)

Winston buys a house for 268 000 pounds. He sells the house for 291 500 pounds. Calculate the percentage profit Winston makes. Give your answer correct to 3 significant figures.

(Total for Question 12 is 3 marks)

Last year an annual rail season ticket cost 3120 pounds. This year it costs 3245 pounds. Work out the percentage increase in the cost of the ticket. Give your answer correct to 1 decimal place.

(Total for Question 13 is 3 marks)

A tenant's monthly rent increases from 850 pounds to 918 pounds. Work out the percentage increase in the rent.

(Total for Question 14 is 3 marks)

A phone was valued at 600 pounds. One year later it was valued at 480 pounds. Work out the percentage decrease in its value.

(Total for Question 15 is 3 marks)

Two shops each had a fall in customer numbers last month. Shop A had 220 customers and now has 187 customers. Shop B had 340 customers and now has 292 customers. Work out which shop had the greater percentage decrease in customers. You must show your working.

(Total for Question 16 is 3 marks)

Yara buys a 5 kg bag of rice for 8 pounds. She repackages it into 250 g bags and sells each bag for 65p. Work out Yara's percentage profit.

(Total for Question 17 is 4 marks)

Callum buys a crate of 60 mangoes for 24 pounds. He finds that 6 of the mangoes are bad and cannot be sold. He sells the remaining mangoes for 70p each. Work out Callum's percentage profit.

(Total for Question 18 is 4 marks)

Priya buys 12 kg of coffee beans for 96 pounds. She packages it into 200 g bags and sells each bag for 1.20 pounds. Work out whether Priya makes a percentage profit or a percentage loss, and calculate it.

(Total for Question 19 is 4 marks)

Aaliyah buys 80 candles for 60 pounds. She sells 50 of the candles for 1.40 pounds each. She sells the remaining candles for 90p each. Work out Aaliyah's percentage profit. Give your answer correct to 1 decimal place.

(Total for Question 20 is 4 marks)

Mark scheme · 3.8 Percentage Change

Question 1

M1 12 seen (52 - 40), or equivalent method
A1 30% cao
Answer: 30%

Question 2

M1 18 seen (90 - 72), or equivalent method
A1 20% cao
Answer: 20%

Question 3

M1 0.50 seen (2.50 - 2)
M1 0.50/2 x 100 (oe)
A1 25% cao
Answer: 25%

Question 4

M1 60 seen (400 - 340)
M1 60/400 x 100 (oe)
A1 15% cao
Answer: 15%

Question 5

M1 12 seen (92 - 80)
M1 12/80 x 100 (oe)
A1 15% cao
Answer: 15%

Question 6

M1 40 seen (250 - 210)
M1 40/250 x 100 (oe)
A1 16% cao
Answer: 16%

Question 7

M1 42 seen (462 - 420)
M1 42/420 x 100 (oe)
A1 10% cao
Answer: 10%

Question 8

M1 185 seen (1380 - 1195)
M1 185/1380 x 100 (oe)
A1 awrt 13.4%
Answer: 13.4%

Question 9

M1 6650 seen (91250 - 84600)
M1 6650/84600 x 100 (oe)
A1 awrt 7.9%
Answer: 7.9%

Question 10

M1 1650 seen (24800 - 23150)
M1 1650/24800 x 100 (oe)
A1 awrt 6.65% (3sf)
Answer: 6.65%

Question 11

M1 1380 seen (9200 - 7820)
M1 1380/9200 x 100 (oe)
A1 15% cao
Answer: 15%

Question 12

M1 23500 seen (291500 - 268000)
M1 23500/268000 x 100 (oe)
A1 awrt 8.77% (3sf)
Answer: 8.77%

Question 13

M1 125 seen (3245 - 3120)
M1 125/3120 x 100 (oe)
A1 awrt 4.0%
Answer: 4.0%

Question 14

M1 68 seen (918 - 850)
M1 68/850 x 100 (oe)
A1 8% cao
Answer: 8%

Question 15

M1 120 seen (600 - 480)
M1 120/600 x 100 (oe)
A1 20% cao
Answer: 20%

Question 16

M1 Shop A: 33/220 x 100 (= 15%)
M1 Shop B: 48/340 x 100 (awrt 14.1%)
A1 Shop A, with correct comparison (15% > 14.1%), oe ft from their two correctly found percentages
Answer: Shop A (15% decrease vs 14.1% decrease)

Question 17

M1 5000/250 = 20 bags
M1 20 x 0.65 = 13 (total revenue)
dM1 13 - 8 = 5 (profit), dependent on both M1s
A1 62.5% cao
Answer: 62.5%

Question 18

M1 60 - 6 = 54 (mangoes sold)
M1 54 x 0.70 = 37.80 (total revenue)
dM1 37.80 - 24 = 13.80 (profit), dependent on both M1s
A1 57.5% cao
Answer: 57.5%

Question 19

M1 12000/200 = 60 bags
M1 60 x 1.20 = 72 (total revenue)
dM1 96 - 72 = 24 (loss), dependent on both M1s
A1 25% loss, cao (must state loss)
Answer: 25% loss

Question 20

M1 50 x 1.40 = 70 and 30 x 0.90 = 27, both seen
M1 70 + 27 = 97 (total revenue)
dM1 97 - 60 = 37 (profit), dependent on both M1s
A1 awrt 61.7%
Answer: 61.7%

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Percentage Change - Worksheets, Questions and Revision

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3.8 Percentage Change

Revision notes: Percentage Change

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