Profit/Loss/Discount (Leaving Cert Mathematics): Revision Notes

Profit, Loss, and Discount

Understanding profit, loss, and discount is an important part of Leaving Cert Maths and everyday financial literacy.
These concepts help us calculate how much money is gained or lost in transactions and how reductions in price (discounts) are expressed as percentages.

When working with these problems, always remember to:

• Identify which price is the Cost Price (C.P.), the Selling Price (S.P.), or the Marked Price (M.P.)
• Use the correct formula for each situation
• Express your final answer clearly, especially when calculating percentages

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Profit

A profit is made when the selling price of an item is greater than the cost price.
This means the seller sells the product for more than it cost to make or buy.

The basic formula for profit is:

$$Profit = Selling \space Price - Cost \space Price$$

To express the profit as a percentage of the cost price, use:

$$Profit \space \% = \frac{Profit}{Cost \space Price} \times 100$$

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Loss

A loss occurs when the selling price is less than the cost price.
This means the seller sells the item for less than it cost to produce or purchase.

The formula for loss is:

$$Loss = Cost \space Price - Selling \space Price$$

To calculate the loss percentage, use:

$$Loss \space \% = \frac{Loss}{Cost \space Price} \times 100$$

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Discount

A discount is a reduction in price, usually offered to encourage customers to buy.
It represents how much less the selling price is than the original or marked price.

The formula for discount is:

$$Discount = Marked \space Price - Selling \space Price$$

To express the discount as a percentage of the marked price, use:

$$Discount \space \% = \frac{Discount}{Marked \space Price} \times 100$$

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Summary

Concept	When It Happens	Formula	Percentage Formula
Profit	Selling Price > Cost Price	$Profit = S.P. - C.P.$	$Profit\% = \frac{Profit}{C.P.} \times 100$
Loss	Selling Price < Cost Price	$Loss = C.P. - S.P.$	$Loss\% = \frac{Loss}{C.P.} \times 100$
Discount	Price reduction from Marked Price	$Discount = M.P. - S.P.$	$Discount\% = \frac{Discount}{M.P.} \times 100$