Percentages

Hong Kong

Stage 1 - Stage 3

Lesson

If you own or work in a business, you need to know whether you're making or losing money. In other words, you need to know whether you're making a profit or a loss.

In this chapter, we'll look at how to calculate profits and losses, as well as how to calculate the percentage profit/ loss.

Terminology

**Profit:** if you make more money than what you spend, you will make a profit.

**Loss:** if you spend more money than what you make, you will register a loss.

**Break- even point:** basically a zero amount, where you spend exact the same amount of money as you earn.

**Revenue:** another name for income or money that is earned by a business.

So, to calculate whether a business will register a profit or a loss, you need to calculate your gross income (ie. all your earnings), as well as the total amount of your expenses. Then you can use the formula:

$\text{gross income }-\text{expenses }=\text{profit/loss }$gross income −expenses =profit/loss

NB. A loss can also be expressed as a negative profit. For example, a profit of $-\$1200$−$1200 would actually mean a loss of $\$1200$$1200.

However, sometimes we know our gross income and our profit so we may want to work out our expenses. We can also use our knowledge of equations to do this. We just sub in the values we know to work out the one we don't.

Percentages are often used in business. For example, it is common to express your profit or loss as a percentage of the buying price (ie. the amount it cost you to buy). To do this, you firstly need to find the profit or loss, like we looked at above. Then, you use the formula:

$\text{percentage profit/ loss }=\frac{\text{profit/loss }}{\text{buying price }}\times100%$percentage profit/ loss =profit/loss buying price ×100%

This is really helpful because it gives you a good indication of how much you are actually making. For example, making $\$100$$100 profit sounds good but is it really that good if you paid $\$100000$$100000 for that item?

Amelia bought a truck for $\$17300$$17300 and sold it four years later, making a loss of $25%$25%. How much did she sell it for?

Xavier bought a property for $\$371000$$371000. In the first year, it increased in value by $12%$12%, but in the second year, it decreased in value by $6%$6%. If running costs during the two years amounted to $\$1500$$1500, find Xavier’s profit or loss at the end of two years.

First, calculate the amount Xavier earned from the changing value of the property. Give your answer correct to the nearest cent.

Now calculate Xavier's total profit. Give your answer correct to the nearest cent.