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Find Percentage Change, Including Profit

In this worksheet students will be able to calculate a percentage change and apply it to problem solving.

'Find Percentage Change, Including Profit' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change, Fractions, Decimals and Percentages

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Percentages

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

 

 

man 

 Sometimes we need to work out  percentage changes.  This helps us work out a percentage profit, or in the case of our friend here a percentage loss.

 

This is one of the annoying areas where we have to learn a formula. Obviously our friend here didn't learn it.  So here goes.

 

Percentage change  = actual change       x 100
                                    original amount

 

You have  put £2500 in the bank 3 years ago.  Now it is worth £2850.  Lucky you.

Using the formula, how can you work out the percentage change?

 

First find the actual change  £2850 - £2500 = 350    Now substitute this into your formula.

Percentage change = actual change   =    £350     x 100    =  14% change
                                   original amount =    £2500

 

Basically that is all there is to it.    You just need to learn the formula.   At least you made a profit.

Don't worry you will have plenty of practice using this.

 


I bet Lord Sugar knows this formula..

 

jacket

That jacket you thought was cool and trendy six months ago, appears a little out of date now.  You decide to sell it.

It cost you £65 and you sell it for £54.  What was the percentage loss you made?  Give your answer to 1 decimal place.

Show your answer as  ....%

You are making  crispy cupcakes for the school fete.  You spend £14.20 on ingredients to make the cup cakes.

You sold all the cakes or a total of £42.90.  What was the percentage profit you made?  Give your answer to 1 decimal place.

Show your answer as .....%

crispy cup cakes

 

cyclist

The members of your cycling club change with members joining and leaving.

Match the percentage change each year  from the information given.  It could be either an increase or decrease.

Round your answers to 1 decimal place.

 

Column A

Column B

Last year 26 members this year 42 members
12%
Last year 42 members this year 38 members
31.6%
Last year 38 members this year 50 members
19.6%
Last year 50 members this year 56
61.5%
Last year 56 members this year 45 members
9.5%

The first figure is the cost price  (original amount) of an item, the second figure is the selling price.  Match up the percentage profit or loss in each case.

Column A

Column B

£20, £25
54%
£60, £54
30%
£460, £598
55.5%
50p, 23p
25%
99p, 44p
10%

Work out the following percentage changes. Show your answers to 1 decimal place (1 d.p)

Write your answers as ...%

 

 

Column A

Column B

£20, £25
54%
£60, £54
30%
£460, £598
55.5%
50p, 23p
25%
99p, 44p
10%

camera

Eye Spy is a shop that sells digital cameras.

In 2017 they sold 678 cameras

In 2018 they sold 735 cameras

Work out the percentage increase in camera sales

Show your answer to 1 decimal place (1.dp)

Write your answer as  ....%

Population of European countries 2017 2018
France 53,245,121 53,321,254
Italy 45,356,123 46,231,895
Portugal 32,675,342 33,452,125

Population changes each year within countries.

Calculate the percentage change for the population of each country.

Give your answers to 2 decimal place (2.dp)

Show your answer as ...%

Piggy bank

You have invested some money in three different banks over two years.  Lucky you.

Which bank has given you the best percentage increase?

  Year 1 Savings Year 2 Savings
Ed Invest £2,500 £2,650
Ben's Bank £1,800 £2,001
Sam's Savings £1,955 £2,312

 

Ed Invest

Ben's Bank

Sam's Savings

An empty watering can weighs 800 g.  it is filled with water and the weight increases to 2.3kg.

What is the percentage change in water in the watering can?

Write your answer to 1 decimal place (1.dp)

Show your answer as ...%

watering can

 

 

beach

Oh fabulous it is holiday time.  You need to change some money.   

The exchange rate at the Post Office is £1  = € 1.12    £1 = $ 1.55

You have come home with  $541 and €135.

The Post office converts you money,  takes their commission and gives you £380.50

What is their percentage commission?  

Show your answer to 2 decimal Places (2.dp)

Write your answer as ....%

  • Question 1

jacket

That jacket you thought was cool and trendy six months ago, appears a little out of date now.  You decide to sell it.

It cost you £65 and you sell it for £54.  What was the percentage loss you made?  Give your answer to 1 decimal place.

Show your answer as  ....%

CORRECT ANSWER
16.9%
EDDIE SAYS
This is just a case of applying the formula. Actual change 65 - 54 = 11 11÷ 65 = 16.9%. Your loss could have been worse. Perhaps the jacket is still cool.
  • Question 2

You are making  crispy cupcakes for the school fete.  You spend £14.20 on ingredients to make the cup cakes.

You sold all the cakes or a total of £42.90.  What was the percentage profit you made?  Give your answer to 1 decimal place.

Show your answer as .....%

crispy cup cakes

 

CORRECT ANSWER
66.9%
EDDIE SAYS
£42.90 -£14.20 = £28.70 28.70 ÷42.90 x 100 = 66.89 (66.9%) to 1 d.p You put the work in so deserve the profit. By the way how many did you eat before the sale?
  • Question 3

cyclist

The members of your cycling club change with members joining and leaving.

Match the percentage change each year  from the information given.  It could be either an increase or decrease.

Round your answers to 1 decimal place.

 

CORRECT ANSWER

Column A

Column B

Last year 26 members this year 42...
61.5%
Last year 42 members this year 38...
9.5%
Last year 38 members this year 5...
31.6%
Last year 50 members this year 56
12%
Last year 56 members this year 45...
19.6%
EDDIE SAYS
Hopefully you are happy using the formula. As mathematicians formulas are great. It is just like following instructions for flat pack furniture, put this here, put that there. Don't be like your dad and ignore the instructions, that is when things fall apart!! 42 - 26 = 16 ÷26 x 100 = 61.5% 42 - 38 =4 ÷ 42 x 100 = 9.5% 50 - 38 = 12÷ 38 x 100 = 31.6% 56 - 50 =6 ÷ 50 x 100 = 12% 56 - 45 =11 ÷ 56 x 100 = 19.6
  • Question 4

The first figure is the cost price  (original amount) of an item, the second figure is the selling price.  Match up the percentage profit or loss in each case.

CORRECT ANSWER

Column A

Column B

£20, £25
25%
£60, £54
10%
£460, £598
30%
50p, 23p
54%
99p, 44p
55.5%
EDDIE SAYS
Always subtract the smaller number from the higher number to get the actual change. Care is needed to make sure we use the original amount. it is not always the largest number 25 - 20 = 5 5 ÷25= 0.25 x 100 = 25% 60 - 54 = 6 6 ÷ 60 = 0.1 x 100 = 10% 598 - 460= 138÷ 460 = 0.3 x 100 = 30% 50 - 23 =27 ÷50 = 0.54 x 100 = 54% 99 - 44 = 55÷99 = 55.5%
  • Question 5

Work out the following percentage changes. Show your answers to 1 decimal place (1 d.p)

Write your answers as ...%

 

 

CORRECT ANSWER
EDDIE SAYS
How easy is it using the formula. The hardest part is learning it! I guess you know the formula pretty well by now, but here is a quick reminder. Largest number minus the smallest number. The your answer and divide it by the original amount before x by 100. e.g 640 - 500 = 140÷ 500=0.28 x 100 = 28% percentage change.
  • Question 6

camera

Eye Spy is a shop that sells digital cameras.

In 2017 they sold 678 cameras

In 2018 they sold 735 cameras

Work out the percentage increase in camera sales

Show your answer to 1 decimal place (1.dp)

Write your answer as  ....%

CORRECT ANSWER
8.4%
EDDIE SAYS
This is an example of how shops can check how well they are doing. I told you percentages are all around us. So you can see why this is a good formula to learn. 735 - 678 = 57 57÷ 735 x 100 = 8.4
  • Question 7
Population of European countries 2017 2018
France 53,245,121 53,321,254
Italy 45,356,123 46,231,895
Portugal 32,675,342 33,452,125

Population changes each year within countries.

Calculate the percentage change for the population of each country.

Give your answers to 2 decimal place (2.dp)

Show your answer as ...%

CORRECT ANSWER
EDDIE SAYS
Oh no large numbers. Don't worry about this the process is still the same. Find the percentage change (large number - small number) Use this change and divide it by the original number and multiply by 100. Job done. As you can see when working with numbers this large the percentage changes tend to be really small.
  • Question 8

Piggy bank

You have invested some money in three different banks over two years.  Lucky you.

Which bank has given you the best percentage increase?

  Year 1 Savings Year 2 Savings
Ed Invest £2,500 £2,650
Ben's Bank £1,800 £2,001
Sam's Savings £1,955 £2,312

 

CORRECT ANSWER
Sam's Savings
EDDIE SAYS
Ah yes another example of how percentage change can help us. Same formula but a different scenario. Banking industry will use this formula a great deal. Ed place 6% Bens Bank 11.2% Sam's Savings 18.3% any chance of a loan?
  • Question 9

An empty watering can weighs 800 g.  it is filled with water and the weight increases to 2.3kg.

What is the percentage change in water in the watering can?

Write your answer to 1 decimal place (1.dp)

Show your answer as ...%

watering can

 

CORRECT ANSWER
187.5%
EDDIE SAYS
Did your eagle eye spot the units of measurement were different? When calculating all units of measurement have to be the same..lets face it it makes life so much easier. 2.3kg = 2300g great now we can apply the formula. 2300 - 800 = 1500 1500 ÷800 = 1.875 1.875 x 100 = 187.5 Percentage changes can go over 100%. So don't worry you have got it wrong. As long as you have applied the formula you will be okay.
  • Question 10

 

beach

Oh fabulous it is holiday time.  You need to change some money.   

The exchange rate at the Post Office is £1  = € 1.12    £1 = $ 1.55

You have come home with  $541 and €135.

The Post office converts you money,  takes their commission and gives you £380.50

What is their percentage commission?  

Show your answer to 2 decimal Places (2.dp)

Write your answer as ....%

CORRECT ANSWER
18.97%
EDDIE SAYS
You are flying now by applying the formula. Sometimes though you have to incorporate other aspects of maths as well to problem solving questions as you would have done here. Note there are two different currencies you have to convert. (well you did choose to go to two different countries) Here goes. To convert from a foreign currency to Pounds sterling always divide. $541÷1.55 = £349.03 €135÷ 1.12 =£120.54 £349.03 + £120.54 = £469.57 (you bough home that much!!) Now apply your percentage change formula. £469.57 - £380.50 = £89.07 £89.07÷£469.57 = 18.97% All that commission.. I say spend it all next time.
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