Percentage increase and decrease can be applied in terms of profit and loss.
When owning or working in a business, we need to know whether the business is making or losing money. In other words, we need to know whether it is making a profit or a loss.
Revenue: Income/money that is earned by a business.
Expenses: Income/money that is spent by a business.
Profit: The surplus remaining after the total costs are deducted from the total revenue. If more money is made than what is spent, a profit will be made.
Loss: The deficit left after the total costs are deducted from the total revenue. If more money is spent than what is made, then the business will register a loss.
Break-even point: When the profit is equal to the costs. When the business spends the exact same amount of money as it earns, the profit is zero and this is the break-even point.
So, to calculate whether a business will register a profit or a loss, we need to calculate the gross income (that is all of the revenue), as well as the total amount of expenses. Then we can use the formula:
$\text{Profit}=\text{total revenue}-\text{total expenses}$Profit=total revenue−total expenses
Note: This formula will express loss as a negative profit. For example, a profit of $-\$1200$−$1200 would actually mean a loss of $\$1200$$1200.
This formula can also be rearranged to find unknown expenditure or revenue. For instance, if we know the revenue and profit we could find the expenses.
Practice questions
Question 1
Calculate the profit (or loss) when:
The selling price is $\$343$$343 and the cost price is $\$134$$134.
The selling price is $\$1697$$1697 and the cost price is $\$2853$$2853.
The money received is $\$470.78$$470.78 and expenses are $\$333.27$$333.27.
The money received is $\$4451.88$$4451.88 and expenses are $\$4520.75$$4520.75.
Question 2
Calculate expenses when:
- the money received is $244 and the profit is $235
The money received is $\$3915$$3915 and the loss is $\$1848$$1848
The money received is $\$883.21$$883.21 and the loss is $\$410.79$$410.79
Calculating percentage profit and loss
It is common to express profit or loss as a percentage of the cost price (i.e. the amount it cost the business to buy). To do this, firstly we need to find the profit or loss, then we use the formula:
$\text{Percentage profit (or loss)}=\frac{\text{profit (or loss)}}{\text{cost price}}\times100%$Percentage profit (or loss)=profit (or loss)cost price×100%
We can also find the percentage profit of the selling price by simply calculating the fraction out of the selling price rather than the cost price.
Question 3
Luke buys a used bike for $\$485$$485 and resells it for $\$690$$690 without spending any money on it.
How much profit did Luke make on the bike?
Now express this profit as a percentage of the original price.
Make sure to give your answer as a percentage, rounding to two decimal places.
Question 4
Justin bought a plasma TV for $\$3720$$3720 and later sold it for $\$3590$$3590.
Express the loss as a percentage of the cost price.
Give your answer correct to one decimal place.
Express the loss as a percentage of the sale price.
Give your answer correct to one decimal place.
question 5
If a good is sold for $3.5$3.5 times its cost price, what is the percentage profit of the sale?