Percentage Profit/Loss/Discount (Junior Cert Mathematics): Revision Notes

Percentage Profit/Loss

What is Percentage Profit?

Percentage profit tells us how much money a business makes compared to how much it cost to buy or make something. It's a way to show profit as a percentage of the cost price.

How to Calculate Percentage Profit:

1. Find the Profit:

• Profit is the extra money you make after selling something for more than it cost.
• Formula: $\text{Profit} = \text{Selling Price} - \text{Cost Price}$
• Example: If a shop buys a jacket for €80 and sells it for €100: $\text{Profit} = 100 - 80 = €20$

2. Calculate the Percentage Profit:

• Formula: $\text{Percentage Profit} = \frac{\text{Profit}}{\text{Cost Price}} \times 100$
• Example: Using the €20 profit: $\frac{20}{80} \times 100 = 25\%$
• Answer: The percentage profit is 25%.

What is Percentage Loss?

Percentage loss happens when something is sold for less than it cost to buy or make. It shows how much money was lost as a percentage of the cost price.

How to Calculate Percentage Loss:

1. Find the Loss:

• Loss is the money lost when selling something for less than it cost.
• Formula: $\text{Loss} = \text{Cost Price} - \text{Selling Price}$
• Example: If a shop buys shoes for €50 but sells them for €40: $\text{Loss} = 50 - 40 = €10$

2. Calculate the Percentage Loss:

• Formula: $\text{Percentage Loss} = \frac{\text{Loss}}{\text{Cost Price}} \times 100$
• Example: Using the €10 loss: $\frac{10}{50} \times 100 = 20\%$
• Answer: The percentage loss is 20%.

What is Percentage Discount?

A discount is a reduction in the price of something. Percentage discount shows how much money is saved compared to the original price.

How to Calculate Percentage Discount:

1. Find the Discount:

• Discount is the amount of money reduced from the original price.
• Formula: $\text{Discount} = \text{Original Price} - \text{Sale Price}$
• Example: If a coat originally costs €60 and is now on sale for €45: $\text{Discount} = 60 - 45 = €15$

2. Calculate the Percentage Discount:

• Formula: $\text{Percentage Discount} = \frac{\text{Discount}}{\text{Original Price}} \times 100$
• Example: Using the €15 discount: $\frac{15}{60} \times 100 = 25\%$
• Answer: The percentage discount is 25%.

Review and Tips:

• Profit happens when the selling price is higher than the cost price.
• Loss happens when the selling price is lower than the cost price.
• Discount happens when the original price is reduced.
• Remember: Always divide by the original or cost price to find the percentage.

Common Mistakes to Avoid:

• Mixing up prices: Always be clear whether you are working with the cost price or the selling price.
• Forgetting the order: When calculating profit, loss, or discount, always subtract the smaller number (usually the cost price) from the larger one (usually the selling price) for profit, and the opposite for loss.
• Incorrect calculations: Carefully follow each step, especially when using a calculator, to avoid simple errors.

Summary of Formulae

Concept	Formula	Explanation
Percentage Profit	$\ \text{Percentage Profit} = \frac{\text{Profit}}{\text{Cost Price}} \times 100$	Shows profit as a percentage of the cost price.
Percentage Loss	$\text{Percentage Loss} = \frac{\text{Loss}}{\text{Cost Price}} \times 100$	Shows loss as a percentage of the cost price.
Percentage Discount	$\text{Percentage Discount} = \frac{\text{Discount}}{\text{Original Price}} \times 100$	Shows the discount as a percentage of the original price.

---