Profit, Loss & Discount

Profit, loss, discount, markup, and tax all compare one amount of money to another. The key is knowing which amount is the base: cost price, selling price, marked price, or discounted price.

CSEC questions often combine these ideas in stages. A product may be marked up, discounted, and then taxed. Work in the order the transaction happens, label each new amount, and state what each percentage is being taken from.

This is where Consumer Arithmetic begins. Every shop, every business, every transaction involves profit, loss, or discount.

Understanding Cost Price and Selling Price¶

Cost Price (CP): The amount a business pays to GET a product.

Selling Price (SP): The amount a customer PAYS for the product.

Profit or Loss is the difference:

• If SP > CP → Profit (business made money)
• If SP < CP → Loss (business lost money)

Calculating Profit and Loss¶

Profit and loss compare what a seller receives with what the seller originally paid. Always start by identifying the cost price and selling price.

Profit = Selling Price - Cost Price $\text{Profit} = SP - CP$

Loss = Cost Price - Selling Price $\text{Loss} = CP - SP$

Profit and Loss as Percentages¶

Percentage profit or loss uses cost price as the base because it measures the gain or loss compared with what the seller invested.

Profit and loss are MORE useful when expressed as percentages. This tells you the actual performance of the business.

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

$\text{Profit \%} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100\%$

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

$\text{Loss \%} = \frac{\text{CP} - \text{SP}}{\text{CP}} \times 100\%$

Understanding Discount¶

A discount reduces the marked price before the customer pays. The discount is usually a percentage of the marked price, not of the final sale price.

Discount: A reduction in price. The shop reduces the selling price to attract customers.

Marked Price (MP): The original price shown on the tag.

Discount: The amount taken OFF the marked price.

Selling Price = Marked Price - Discount $\text{SP} = \text{MP} - \text{Discount}$

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

$\text{Discount \%} = \frac{\text{MP} - \text{SP}}{\text{MP}} \times 100\%$

Markup¶

Markup is added to cost price to create a selling price. Businesses use markup to cover expenses and make profit.

Markup: A percentage increase added to cost price to get the marked (selling) price.

$\text{Marked Price} = \text{Cost Price} + \text{Markup}$

Or as a percentage:

$\text{Markup \%} = \frac{\text{MP} - \text{CP}}{\text{CP}} \times 100\%$

Sales Tax¶

Sales tax is added after the selling price or discounted price has been found. If a discount comes first, calculate tax on the reduced price unless the question says otherwise.

Sales Tax: Money added to the price — usually collected by the government.

Amount after tax = Original Price + Sales Tax

If tax is $t\%$:

$\text{Total Price} = \text{Price} + \frac{t}{100} \times \text{Price}$

Or more simply:

$\text{Total Price} = \text{Price} \times \left(1 + \frac{t}{100}\right)$

---

Part 2: Solving Complex Profit/Loss Problems¶

Now let's combine these concepts. Real-world problems often involve multiple steps.

Finding Missing Values¶

Missing-value questions work backward. Write the usual formula first, substitute what you know, and solve for the unknown.

Sometimes you're given profit %, profit amount, or selling price — and need to find other values.

Key Formulas to Remember:

• $\text{SP} = \text{CP} + \text{Profit}$
• $\text{CP} = \text{SP} - \text{Profit}$
• $\text{Profit \%} = \frac{\text{Profit}}{\text{CP}} \times 100\%$