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Fractions, decimals and percentages One number as a percentage of another Percentage changeThis topic is relevant for:

Here we will learn about percentage profit, including what percentage profit is and how to solve problems involving percentage profit.

There are also percentage profit worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

**Percentage profit** is writing a profit as a percentage. This makes it easier to compare with other profits.

To do this you need to find the profit and change this into a percentage of the original amount (the cost of the item at the start). Calculating profit is done by finding the difference between the cost price and the selling price.

You can use this formula to calculate the profit percentage,

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100 .

For example, I bought a painting for £200. I sold it for £230. So the profit I have made is £30 as this is the difference between the cost price and the selling price.

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{30}{200}\times 100=15\%The percentage profit is 15\%.

The amount of money the item is **bought **for at the start can be called the** cost price **(or cost of goods sold).

The amount of money the item is **sold **for later in the question can be called the **sale price** or the **selling price**.

This can be extended into calculating percentage loss. This is when the value has gone down over time (known as depreciation).

\text{Percentage loss}=\cfrac{\text{loss}}{\text{original}}\times 100This skill is very useful for business owners.

In order to calculate percentage profit:

**Calculate the difference between the cost price and the selling price.****Express the profit (or loss) as a fraction of the original amount and multiply by**\bf{100}**.****Write down the final answer.**

Get your free percentage profit worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free percentage profit worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREERon bought an antique train set for £130.

He sold it for £215.

Calculate the percentage profit Ron made.

Give your answer to the nearest percent.

**Calculate the difference between the cost price and the selling price.**

The difference is,

215-130=85.2**Express the profit (or loss) as a fraction of the original amount and multiply by ** \bf{100} **.**

You can find the percentage profit by making a fraction and multiplying by 100.

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{85}{130}\times 100=65.384…3**Write down the final answer.**

The percentage profit Ron made is \bf{65\%} to the nearest percent.

Ellen buys a house for £210 \ 000. She sells the house for £226 \ 500.

Calculate the percentage profit Ellen makes. Give your answer to 1 decimal place.

**Calculate the difference between the cost price and the selling price.**

The difference is,

226 \ 500-210 \ 000=16 \ 500.

**Express the profit (or loss) as a fraction of the original amount and multiply by ** \bf{100} **.**

You can find the percentage profit by making a fraction and multiplying by 100.

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{16 \ 500}{210 \ 000}\times 100=7.857…

**Write down the final answer.**

The percentage profit Ellen makes is \bf{7.9\%} to 1 decimal place.

Diane bought an antique vase for £95.

She sold it for £78.

Calculate the percentage loss Diane made.

Give your answer to 3 significant figures.

**Calculate the difference between the cost price and the selling price.**

The difference is,

95-78=17.

**Express the profit (or loss) as a fraction of the original amount and multiply by ** \bf{100} **.**

You can find the percentage loss by making a fraction and multiplying by 100.

\text{Percentage loss}=\cfrac{\text{loss}}{\text{original}}\times 100=\cfrac{17}{95}\times 100=17.894…

**Write down the final answer.**

The percentage loss Diane made is \bf{17.9\%} to 3 significant figures.

Rahul bought a van for £16 \ 500.

He sold it for £9 \ 350.

Calculate the percentage loss Rahul made.

Give your answer to 3 significant figures.

**Calculate the difference between the cost price and the selling price.**

The difference is,

16 \ 500-9 \ 350=7 \ 150.

**Express the profit (or loss) as a fraction of the original amount and multiply by ** \bf{100} **.**

You can find the percentage loss by making a fraction and multiplying by 100.

\text{Percentage loss}=\cfrac{\text{loss}}{\text{original}}\times 100=\cfrac{7 \ 150}{16 \ 500}\times 100=43.333…

**Write down the final answer.**

The percentage loss Rahul makes is \bf{43.3\%} to 3 significant figures.

Katie buys a pack of 12 bottles of water for £3.50.

She sells the water at 80p per bottle.

Work out Katie’s percentage profit.

Give your answer to 3 significant figures.

**Calculate the difference between the cost price and the selling price.**

First you need to calculate the total selling price (or total sales).

12\times 80=960

The total selling price is £9.60

The difference is,

£9.60-£3.50=£6.10 .

**Express the profit (or loss) as a fraction of the original amount and multiply by ** \bf{100} **.**

You can find the percentage profit by making a fraction and multiplying by 100.

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{6.10}{3.50}\times 100=174.285…

**Write down the final answer.**

The percentage profit Katie makes is \bf{174\%}.

Ranjeev buys 20 jackets at £25 each.

He sells 15\% of them for £50 each and half of them for £35. He sells the rest for £12 each.

Work out Ranjeev’s percentage profit or loss.

State clearly if Ranjeev makes a profit or a loss.

Give your answer to 3 significant figures.

**Calculate the difference between the cost price and the selling price.**

First you need to calculate the total cost price (or cost of goods sold).

20\times \pounds25=\pounds500

Then you need to work out the total selling price (or total sales).

15\% of 20 is 3 jackets, so he sells 3 jackets at £50. He also sells 10 jackets at £35 and 7 jackets at £12.

The total selling price is,

(3\times \pounds50) + (10\times \pounds35) + (7\times \pounds12)=\pounds584.

Ranjeev sells the jackets for more than he bought them for, so he has made a profit.

The difference is,

584-500=84 .

**Express the profit (or loss) as a fraction of the original amount and multiply by ** \bf{100} **.**

You can find the percentage profit by making a fraction and multiplying by 100.

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{84}{500}\times 100=16.8

**Write down the final answer.**

Ranjeev makes a **profit** and the percentage profit is \bf{16.8\%}.

**Always use the original cost price as the denominator**

The original cost price is always used as the denominator in the percentage formula for profit.

**Be consistent with pounds and pence**

Sometimes questions may give one amount of money in pence (p), and another amount of money in pounds (£). When you calculate the percentage profit (or loss) make sure you use the same type of monetary units in your fraction. Whichever you use will give the same percentage profit.

\bf{100}**Percentage profits can be more than**

When calculating percentages for profits, they can be greater than 100\%. For example, if I buy a bottle of water for £0.50 and I sell it for £2, I made £1.50 profit which is 300\% profit. I sold the bottle for 4 times more than I originally bought it for.

Reverse percentages is part of our series of lessons to support revision on percentages. You may find it helpful to start with the main percentages lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

1. A trailer is bought for £50 and is sold for £60. Find the percentage profit.

20\%

2\%

16.7\%

17\%

The profit is £10.

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{10}{50}\times 100=20

The percentage profit is 20\%.

2. A flat is bought for £120 \ 000 and is sold for £145 \ 000. Find the percentage profit. Give your answer to the nearest percent.

25\%

17\%

28\%

21\%

The profit is £25 \ 000.

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{10}{50}\times 100=20.8333…

The percentage profit is 21\% (to the nearest percent).

3. A motorbike is bought for £995 and is sold for £850. Find the percentage loss. Give your answer to the nearest percent.

14\%

15\%

16\%

17\%

The loss is £145.

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{145}{995}\times 100=14.572…

The percentage loss is 15\% (to the nearest percent).

4. A flat is bought for £120 \ 000 and is sold for £106 \ 500. Find the percentage loss. Give your answer to the nearest percent.

11\%

12\%

13\%

10\%

The loss is £13500.

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{13500}{120000}\times 100=11.25

The percentage loss is 11\% (to the nearest percent).

5. Molly buys 24 packets of crisps for £8.95. She sells the packets of crisps for 50p each. Calculate the percentage profit. Give your answer to 3 significant figures.

25.5\%

25.4\%

34.0\%

34.1\%

The selling price of the crisps is,

24\times \pounds0.50=\pounds12.

The profit is £3.05.

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{3.05}{8.95}\times 100=34.078…

The percentage profit is 34.1\% (to 3 significant figures).

6. Yago buys 200 books for £4 each. He sells \cfrac{3}{4} of the books for £6.50 each and the rest for £1 each. Calculate the percentage profit or loss, stating clearly if there is a profit or a loss. Give your answer to one decimal place.

Loss 28.1\%

Profit 28.1\%

Loss 21.8\%

Profit 21.8\%

The cost of the books is,

200\times \pounds4=\pounds800 .

The selling price of the books is,

(150\times \pounds6.50)+(50\times \pounds1)=\pounds1025 .

The profit is £225.

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{225}{800}\times 100=28.125

The percentage profit is 28.1\% (to the nearest percent).

1. A small business buys phones for £45 each and sells them for £75.

Calculate the percentage profit for each phone. Give your answer to 1 decimal place.

**(3 marks)**

Show answer

75-45=30

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2. (a) Malcolm buys a bike for £800.

He sells it to Gordon for £500.

Calculate Malcolm’s percentage loss.

(b) Gordon then sells the bike to Samir for £540.

Calculate Gordon’s percentage profit.

**(5 marks)**

Show answer

(a)

800-500=300

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(b)

\cfrac{540-500}{500}\times 100=\cfrac{40}{500}\times 100

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3. Sundeep is a business owner of a small business.

He buys 40 games consoles at £65 each.

He sells a quarter of the games consoles for £100 each.

He sells 35\% of the games consoles for £75 each.

He sells the rest for £30 each.

Calculate the percentage profit or loss for Sundeep.

State clearly if it is a percentage profit or loss.

Give your answer correct to 3 significant figures.

**(6 marks)**

Show answer

40\times \pounds65=\pounds2600

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LOSS of 2.69\%

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You have now learned how to:

- Calculate percentage profit
- Calculate percentage loss
- Solve problems involving percentage profit

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