# Profit and Loss

## Profit:

A profit is an amount of money added to the original price.
The price with the added profit is more expensive than the original price.

Useful rules are:

• Profit = Percent Profit × Original Price
• Price with Profit = Original Price + Profit
• Percent Profit = Profit ÷ Original Price × 100

## Example One - Price with Profit

A t-shirt store makes a profit of 35%. What is the price with profit for a t-shirt whose original price is \$20?

Profit
= Percent Profit × Original price
= 35% × \$20
= \$7

Price with profit
= Original Price + Profit
= \$20 + \$7
= \$27

The original price is 100%.
If the profit is 35%, then the price with profit = 100% + 35% = 135%.
Price with profit
= 135% of \$20
= \$27

## Example Two - Finding Percent Profit

If a car keyless entry remote ("beeper") is lost, the replacement cost is \$80. However, the cost of the software by the supplier is \$10. What is the profit? What is the percent profit?

Profit
= \$80 – \$10
= \$70

Percent Profit
= Profit ÷ Original Price × 100
= \$70 ÷ \$10 × 100
= 700%

## Example Three - Finding Original Price

A profit of 30% is equal to \$26. What was the original price?

Price with Profit
= 100% + 30%
= 130%

Original Price
= \$26 × 100 ÷ 130
= \$20

## Questions - Profit

Q1. A store makes a profit of 40%. What is the price after profit of a skateboard originally priced at \$60?
Q2. The original price of a football was \$30. The added profit is \$18. What is the percent profit?
Q3. A volleyball sold for \$15 after a profit of 50% was added. What is the original price?

A1. \$84
A2. 60%
A3. \$10

## Loss:

A loss is an amount of money subtracted from the original price.
The price minus the loss is cheaper than the original price.
The calculations for loss are the same as for discount.

## Questions - Loss

Q1. A store makes a loss of 40% on fluoro-coloured socks. If the original price was \$6, what is the new price?
Q2. The original price of storm-damaged plants was \$80. If they sold for \$60, what was the percent profit?
Q3. Retro-style flared trousers sold for \$15. The loss was 80%. What is the original price?   