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.

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.

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$$100 profit sound good but is it really that good if you paid $\$100000$$100000 for that item.

Calculate the sale price of an item if:

**A)** the cost price was $\$305$$305 and the profit made was $\$224$$224

**Think:** A profit indicates that the item was sold for more than the cost price.

**Do:** $305+224=\$529$305+224=$529

**B)** the cost price was $\$275$$275 and the loss on the sale was $\$139$$139

**Think:** A loss indicates that the item was sold for less than the cost price.

**Do:** $275-139=\$136$275−139=$136

A retailer purchased a refrigerator for $\$270$$270 and sold it for $\$310$$310. Calculate the profit as a percentage of the cost price, expressing your answer as a percentage correct to two decimal places.

**Think:** Firstly we need to calculate the profit, then we can express it as a percentage.

**Do:**

Firstly, we'll work out the profit:

$310-270=\$40$310−270=$40

Then we'll use this answer and express it as a percentage:

$\frac{40}{270}\times100%$40270×100% | $=$= | $14.814$14.814... |

$=$= | $14.81%$14.81% |

A pair of socks costs a salesman $£1.69$£1.69 to make and he is taxed $25%$25% of the profit he makes from the sale.

If he sells each pair of socks at $£P$£

`P`, write an expression in terms of $P$`P`for his after-tax profit per pair of socks.If the salesman wishes to make an after-tax profit of $33%$33%, calculate the price, $£P$£

`P`, to the nearest penny, at which he must sell each pair of socks.