How to use this guide
Read each section carefully and follow the worked examples. Pay attention to how cost and selling prices are used to determine profit or loss step by step.
Big idea: Profit occurs when selling price is greater than cost price, while loss occurs when selling price is less than cost price.
What is Cost Price?
\[
CP = \text{Cost Price}
\]
Cost Price is the amount paid to buy an item.
Example:
\[
CP = \$50
\]
This means the item was bought for $50.
If an item costs $80, what is its cost price?
\[ CP = 80 \]What is Selling Price?
\[
SP = \text{Selling Price}
\]
Selling Price is the amount for which an item is sold.
Example:
\[
SP = \$100
\]
This means the item was sold for $100.
Profit
\[
\text{Profit} = SP - CP
\]
Profit occurs when the selling price is greater than the cost price.
Example:
\[
SP = 120,\quad CP = 100
\]
\[
\text{Profit} = 120 - 100 = 20
\]
Loss
\[
\text{Loss} = CP - SP
\]
Loss occurs when the cost price is greater than the selling price.
Example:
\[
CP = 150,\quad SP = 120
\]
\[
\text{Loss} = 150 - 120 = 30
\]
Profit Formula
\[
\text{Profit} = SP - CP
\]
Solve:
\[
CP = 200,\quad SP = 260
\]
\[
\text{Profit} = 260 - 200 = 60
\]
Try This Question
Loss Formula
\[
\text{Loss} = CP - SP
\]
Solve:
\[
CP = 300,\quad SP = 250
\]
\[
\text{Loss} = 300 - 250 = 50
\]
Profit Percentage
\[
\text{Profit \%} = \frac{\text{Profit}}{CP} \times 100
\]
Example:
\[
\text{Profit} = 20,\quad CP = 100
\]
\[
\text{Profit \%} = \frac{20}{100} \times 100 = 20\%
\]
Try This Question
Loss Percentage
\[
\text{Loss \%} = \frac{\text{Loss}}{CP} \times 100
\]
Example:
\[
\text{Loss} = 30,\quad CP = 150
\]
\[
\text{Loss \%} = \frac{30}{150} \times 100 = 20\%
\]
Mixed Practice
Find Profit:
\[
CP = 90,\quad SP = 120
\]
\[
\text{Profit} = 30
\]
Find Loss:
\[
CP = 200,\quad SP = 150
\]
\[
\text{Loss} = 50
\]
Find Profit %:
\[
\text{Profit} = 40,\quad CP = 200
\]
\[
20\%
\]