# Find Percentage Change, Including Profit

In this worksheet, students will calculate a percentage change using the relevant formula and apply this to real-life scenarios.

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:

### QUESTION 1 of 10

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 areas where we have to learn a formula - obviously our friend here didn't learn it!

So here goes:

 Percentage change = Actual change × 100 Original amount

e.g. Imagine you put £2500 in the bank 3 years ago, and now it is worth £2850 - lucky you!

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

First let's find the actual change:

2850 - 2500 = £350

Now substitute this value into our formula.

 Percentage change = Actual change × 100 = 350 × 100 = 14% increase Original amount = 2500

Basically that is all we need to do - we just need to learn the formula.

Don't worry you will have plenty of practice using this in the rest of this activity, as we apply the formula to find percentage increases and decreases.

You may want to have a pen and paper handy to record your working, so you can compare what you have with the examples written by our maths teacher. You will also need a calculator.

At least you made a profit in this example!

Let's see how we get on in the rest of this activity...

That jacket you thought was cool and trendy six months ago, appears a little out of date now, so you have decided to sell it.

It cost you £65 and you sell it for £54.

What was the percentage loss you made?

You are making crispy cupcakes for the school fete.

You spend £14.20 on ingredients to make the cupcakes.

You sold all the cupcakes for a total of £42.90.

What was the percentage profit you made?

The total membership of your cycling club changes as members join and leave.

Match the percentage change from each year with the information given.

All percentages have been rounded to 1 decimal place.

## Column B

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

In the pairs of figures on the left, the first is the cost price of an item (the original amount) and the second is the selling price

Match each percentage profit or loss to its correct prices.

## Column B

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

Complete the gaps below to express the following percentage changes.

## Column B

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

i-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 between the two years.

## Column B

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

This table shows population changes each year within some European countries:

 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

Calculate the percentage change for the population of each country.

## Column B

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

You have invested some money in three different banks over two years - lucky you!

Which bank has given you the best percentage increase based on the table below?

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

Betty's Bank

Sam's Savings

An empty watering can weighs 800 g.

It is filled with water and the weight increases to 2.3 kg.

What is the percentage change in the weight of the watering can?

Ed Invest

Betty's Bank

Sam's Savings

Oh fabulous, it is holiday time!

When you return, you need to change some leftover local currency back into pounds.

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

You have come home with \$541 and €135.

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

What is their percentage commission overall?

Ed Invest

Betty's Bank

Sam's Savings

• Question 1

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

It cost you £65 and you sell it for £54.

What was the percentage loss you made?

EDDIE SAYS
Let's apply our formula in this first question: Actual change ÷ Original amount × 100 = % change We know our original amount is £65. Our actual change can be calculated like this: 65 - 54 = 11 Now let's apply our formula: 11÷ 65 × 100 = 16.9% Don't forget to round your answer to 1 decimal place. Your loss could have been worse - perhaps that jacket is still cooler than you thought!
• Question 2

You are making crispy cupcakes for the school fete.

You spend £14.20 on ingredients to make the cupcakes.

You sold all the cupcakes for a total of £42.90.

What was the percentage profit you made?

EDDIE SAYS
Let's find our actual change to input to our formula: £42.90 - £14.20 = £28.70 Now let's apply our formula: 28.70 ÷ 42.90 × 100 = 66.9 to 1 d.p. You put the work in, so you deserve this profit!
• Question 3

The total membership of your cycling club changes as members join and leave.

Match the percentage change from each year with the information given.

All percentages have been rounded to 1 decimal place.

## Column B

Last year 26 members, this year 4...
61.5%
Last year 42 members, this year 3...
9.5%
Last year 38 members, this year 5...
31.6%
Last year 50 members, this year 5...
12%
Last year 56 members, this year 4...
19.6%
EDDIE SAYS
Hopefully you are happy using this formula for % change now. As mathematicians, formulas are great. It is just like following instructions for flat-pack furniture - put this here, put that there... Don't be one of those silly people who ignore the instructions, as this is when things fall apart! Your working for each scenario should look something like this: 42 - 26 = 16 ÷ 26 × 100 = 61.5% increase 42 - 38 = 4 ÷ 42 × 100 = 9.5% decrease 50 - 38 = 12÷ 38 × 100 = 31.6% increase 56 - 50 = 6 ÷ 50 × 100 = 12% increase 56 - 45 =11 ÷ 56 × 100 = 19.6 decrease How did you do?
• Question 4

In the pairs of figures on the left, the first is the cost price of an item (the original amount) and the second is the selling price

Match each percentage profit or loss to its correct prices.

## 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 find the actual change. Care is sometimes needed to identify the original amount, it is not always the largest number. 25 - 20 = 5 (actual change) 5 ÷ 20 × 100 = 25% profit 60 - 54 = 6 6 ÷ 60 × 100 = 10% loss 598 - 460 = 138 138 ÷ 460 × 100 = 30% profit 50 - 23 = 27 27 ÷ 50 × 100 = 54% loss 99 - 44 = 55 55 ÷ 99 × 100 = 55.5% loss Remember we will have made a profit if we sell our item for more than we bought it for, whilst we will have made a loss if the opposite is true. Which would you prefer?!
• Question 5

Complete the gaps below to express the following percentage changes.

EDDIE SAYS
How easy is it using the formula - the hardest part is just remembering it! Here is a quick reminder: Take the largest number and minus the smallest number. Then take your answer and divide it by the original amount before multiplying by 100. Let's look at the first one together to check you have this down: Original amount = £500 Actual change = 640 - 500 = £140 140 ÷ 500 × 100 = 28% profit - that's not bad at all! Can you use this example to apply the formula independently in the other scenarios to find the % change in each case?
• Question 6

i-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 between the two years.

EDDIE SAYS
This is an example of how shops can check how well they are doing as a business. Let's apply our formula to help them out. Original amount = 678 Actual change = 735 - 678 = 57 57 ÷ 678 × 100 = 8.4 to 1 d.p. How well do you think they are doing as a business? Would you be happy with this increase in sales?
• Question 7

This table shows population changes each year within some European countries:

 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

Calculate the percentage change for the population of each country.

EDDIE SAYS
Oh no large numbers! Don't worry about this, as our process is still exactly the same. Don't forget to use your calculator to help you out. Let's work out France's change together, and then you can apply this process to Italy and Portugal. Original amount = 53,245,121 Actual change = 53,321,254 - 53,245,121 = 76,133 76,133 ÷ 53,245,121 × 100 = 0.14% to 2 d.p. Did you type those large numbers in carefully on your calculator? As you can see, when we are working with numbers this large, the percentage changes tend to be really small.
• Question 8

You have invested some money in three different banks over two years - lucky you!

Which bank has given you the best percentage increase based on the table below?

 Year 1 Savings Year 2 Savings Ed Invest £2,500 £2,650 Betty's Bank £1,800 £2,001 Sam's Savings £1,955 £2,312
Sam's Savings
EDDIE SAYS
Ah yes, another example of how understanding percentage changes can really help us in everyday life. The banking industry will use this formula a great deal. We calculate our rates by dividing the change between the 2 years by our original amount. Let's look at Ed Invest together: Original amount = 2500 Actual change = 2650 - 2500 = 150 150 ÷ 2500 × 100 = 6% increase Can you follow this pattern to find the increases for Betty and Sam's banks? Betty's Bank = 11.2% Sam's Savings = 18.3% So which bank gave you the best percentage increase? Perhaps you should move all your money into her for next year!
• Question 9

An empty watering can weighs 800 g.

It is filled with water and the weight increases to 2.3 kg.

What is the percentage change in the weight of the watering can?

EDDIE SAYS
Did your eagle eyes spot that the units of measurement were different here? When calculating with units of measurement, we need to make sure that they the same... let's face it, this makes life so much easier! 2.3 kg = 2300g Great, now we have both amounts in grams, we can apply the formula as usual. Original amount = 800 Actual change = 2300 - 800 = 1500 1500 ÷ 800 × 100 = 187.5% Percentage changes often go over 100%, so don't worry that you have got it wrong if this is the case.
• Question 10

Oh fabulous, it is holiday time!

When you return, you need to change some leftover local currency back into pounds.

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

You have come home with \$541 and €135.

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

What is their percentage commission overall?

EDDIE SAYS
Sometimes you have to incorporate other aspects of maths into problem solving questions. Here, there are two different currencies which we must convert. Here goes... To convert from a foreign currency to pounds always divide: \$541 ÷ 1.55 = £349.03 €135 ÷ 1.12 =£120.54 £349.03 + £120.54 = £469.57 is the amount you returned home with - that was very frugal of you! Now we can apply our percentage change formula as normal. Original amount: £380.50 Actual change: 469.57 - 380.50 = £89.07 £89.07 ÷ £469.57 × 100 = 18.97% All that commission to pay... we say spend it all next time! Congratulations on completing this activity! Hopefully you have seen all the ways in which percentages play a role in our everyday lives, as well as perfecting how to apply the formula for percentage change accurately.
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