Learning Objectives
- distinguish cost price and selling price;
- calculate profit and loss;
- find profit and loss percentages;
- understand mark-up and margin;
- solve business and shopping problems.
Introduction
This lesson develops Profit, Loss and Mark-up from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
🏪 Interactive Profit and Loss Shop
Change the cost price and selling price to see when the shop makes a profit or a loss.
Profit
Percentage based on cost price
Price scale
Cost price
Selling price
$0$175$350$525$700
Notice that profit or loss percentage normally uses cost price as the denominator.
🌍 Where Will You Use This?
Every shop and business must compare what an item costs with what it earns from selling it. This determines whether the transaction makes a profit or loss.
The Three Important Prices
Profit and Loss
Profit = SP − CP
Loss = CP − SP
Profit occurs when SP > CP. Loss occurs when SP < CP.
Profit and Loss Percentages
Profit % = Profit ÷ Cost Price × 100%
Loss % = Loss ÷ Cost Price × 100%
Profit and loss percentages are normally based on cost price unless the
question clearly states otherwise.
Worked Example 1: Profit
A trader buys a chair for US$48 and sells it for US$66.
1
Profit = 66−48 = US$18.
2
Profit % = 18/48×100 = 37.5%.
Worked Example 2: Loss
A phone bought for US$250 is sold for US$215.
1
Loss = 250−215 = US$35.
2
Loss % = 35/250×100 = 14%.
Mark-up
Mark-up is the amount added to cost price to obtain the selling price.
Selling Price = Cost Price × (1 + mark-up rate)
A shop adds a 30% mark-up to an item costing US$80.
SP = 80×1.30 = US$104.
Margin Is Different
Profit margin expresses profit as a percentage of selling price, while mark-up expresses profit as a percentage of cost price.
| Measure | Denominator |
|---|---|
| Mark-up / profit percentage | Cost price |
| Profit margin | Selling price |
Discount After Mark-up
An item costs US$100. It is marked up by 40%, then discounted by 10%. Find the final selling price.
1
Marked price = 100×1.40 = US$140.
2
Final price = 140×0.90 = US$126.
3
Profit = 126−100 = US$26.
💼 Money Smart Tip
A discount does not automatically mean the seller makes a loss. A product may first have been marked up above cost price.
🔍 How Do I Recognise the Required Calculation?
- SP greater than CP → profit.
- SP lower than CP → loss.
- “Mark-up on cost” → percentage of CP.
- “Margin” → percentage of SP.
- Successive mark-up and discount → use multipliers in order.
✅ Quick Check
CP=US$60, SP=US$75. Find profit.
Find the profit percentage for the same item.
Mark up US$200 by 25%.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Practice Questions
Foundation- An item costs US$36 and sells for US$45. Find profit and profit percentage.
- An item costs US$125 and sells for US$110. Find loss and loss percentage.
- A product costs US$72. Find its selling price after a 25% mark-up.
- A trader wants a 20% profit on an item costing US$85. Find the required selling price.
- An item is sold for US$144 after a 20% profit. Find its cost price.
- A product costing US$160 is marked up by 35%, then discounted by 15%. Find the final price and profit percentage.
- A shop sells an item at a 20% discount on its marked price and still makes a 28% profit on cost. The cost is US$150. Find the marked price.
✅ Check Your Work
Show practice answers
- Profit US$9; profit percentage 25%.
- Loss US$15; loss percentage 12%.
- US$90.
- US$102.
- US$120.
-
Final price = 160×1.35×0.85 = US$183.60.
Profit = US$23.60; profit percentage = 14.75%. -
Required selling price = 150×1.28 = US$192.
80% of marked price = 192.
Marked price = 192÷0.80 = US$240.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Profit = SP−CP; loss = CP−SP.
- Profit and loss percentages normally use cost price.
- Mark-up is added to cost price.
- Margin uses selling price as its denominator.
- Apply successive price changes in order.