Profit and loss - Intermediate and Higher tier
When a company makes money after it pays all its costs, it is said to have made a profit. If a company does not make enough money to cover all its costs, it is said to have made a loss.
Question
A company buys stock at £3,250 and sells it at £4,150. How much profit does it make on this stock?
£4,150 – £3,250 = £900 profit.
Question
Last year a shop received £120,000 in takings. This table shows the shop’s expenditure.
| Detail | Amount |
| Building rental | £12,000 |
| Salaries | £48,000 |
| Cost of stock | £55,000 |
| Other | £16,000 |
| Detail | Building rental |
|---|---|
| Amount | £12,000 |
| Detail | Salaries |
|---|---|
| Amount | £48,000 |
| Detail | Cost of stock |
|---|---|
| Amount | £55,000 |
| Detail | Other |
|---|---|
| Amount | £16,000 |
Is the shop currently making a profit or a loss?
Total expenditure:
£12,000 + £48,000 + £55,000 + £16,000 = £131,000
£120,000 takings – £131,000 expenditure = -£11,000
This means they are making a loss of £11,000.
Example
A company pays £100 for a mobile phone. During a summer sale, the company offers a 20% discount on the normal marked price of the phone. The company is still making a 10% profit during the sale. What is the marked price before the discount is applied?
Find out what the sale price of the phone is to make 10% profit for the company:
10% profit = 10% of 100 = £10
Sale price is £100 + £10 = £110
The sale price of the phone was the original amount which has been reduced by 20%.
So the sale price is therefore 80% of the original amount (100% - 20% = 80%).
If we find out what 1% is worth we could then multiply it by 100 to find the original amount.
80% = 110
1% = 110 ÷ 80 = 1.375
Therefore, 100% = 1.375 × 100 = £137.50
Percentage profit or loss
You are often asked in maths to give a percentage profit or loss. The formula to calculate percentage profit is:
\({Percentage~profit} = \frac {Profit} {Original~Amount}~\times~{100}\)
Similarly, percentage loss can be found using this formula:
\({Percentage~loss} = \frac {Loss} {Original~Amount}~\times~{100}\)
Example
The manager of a shoe company buys 20 pairs of trainers for £40 each.
1. Find the percentage profit if the trainers are sold for £50 each.
2. Find the percentage loss if the trainers are sold for £35 each.
Solution
1. Total cost of trainers: 20 × £40 = £800.
Total selling price: 20 × £50 = £1,000.
Profit: £1,000 – £800 = £200.
\({Percentage~profit} = \frac {Profit} {Original~Amount}~\times~{100}\)
\({Percentage~profit} = \frac {200} {800}~\times~{100}~=~25\percent\)
You would have had the same answer if you’d worked out the formula by only using the information for one pair:
Profit: £50 – £40 = £10.
\({Percentage~profit} = \frac {Profit} {Original~Amount}~\times~{100}\)
\({Percentage~profit} = \frac {10} {40}~\times~{100}~=~25\percent\)
2. We will only use the information for one pair this time.
Loss: £40 – £35 = £5.
\({Percentage~loss} = \frac {Loss} {Original~Amount}~\times~{100}\)
\({Percentage~loss} = \frac {5} {40}~\times~{100}~=~12.5\percent\)
Question
Calculate the percentage loss if a company buys stock for £1,000 but only manages to sell it for £900.
Loss: 1,000 – 900 = £100.
\({Percentage~loss} = \frac {Loss} {Original~Amount}~\times~{100}\)
\({Percentage~loss} = \frac {100} {1000}~\times~{100}~=~10\percent\)
They make a 10% loss.
