Profit and Loss Lesson - Concepts, Formula, Definition, Calculation, Examples

Lesson Overview

• What Is Profit and Loss?
• Profit and Loss Basic Concepts
• Profit and Loss Formulas
• How to Calculate Profit and Loss
• Profit and Loss Examples
• Profit and Loss Percentage Formula
• Profit and Loss Tricks
• Profit & Loss Assessment

What Is Profit and Loss?

Profit and loss are used to calculate how much money is gained or lost when buying and selling something.

• Profit happens when the selling price (SP) is higher than the cost price (CP).

Loss happens when the cost price (CP) is higher than the selling price (SP).

Profit and Loss Basic Concepts

Understanding profit and loss is important for making good business decisions. Here are the key ideas:

• Cost Price (C.P.): The price at which something is bought.
• Selling Price (S.P.): The price at which something is sold.
• Profit: When S.P. is more than C.P.
• Loss: When S.P. is less than C.P.
• Profit Percentage: How much profit you made compared to the cost price.

Loss Percentage: How much loss you had compared to the cost price.

Take This Quiz :

Profit and Loss- Chapter wise Test

Profit and Loss Formulas

Here are the main formulas to calculate profit and loss:

How to Calculate Profit and Loss

To calculate profit or loss, follow these steps:

Step: 1. Write down the Cost Price (CP) and Selling Price (SP) from the question.

Step: 2. Check if SP > CP or CP > SP:

• If SP > CP, use the Profit Formula: Profit = SP - CP
• If CP > SP, use the Loss Formula: Loss = CP - SP

Step: 3. Use percentage formulas if required:

• Profit % = (Profit / CP) × 100
• Loss % = (Loss / CP) × 100

Take This Quiz :

Math Quiz: How Much You Can Score In Profit And Loss Test?

Profit and Loss Examples

Let us see some examples:

Example 1: Finding Profit

Question: A student buys a notebook for $20 and sells it for $25. What is the profit?

• Solution:
  • Cost Price (CP) = $20
  • Selling Price (SP) = $25
  • Profit = SP - CP = 25 - 20 = $5

Explanation:
The notebook was bought for $20 and sold for $25, so the student earned $5 as profit.

Example 2: Finding Loss

Question: A shopkeeper buys a shirt for $50 and sells it for $45. What is the loss?

• Solution:
  • Cost Price (CP) = $50
  • Selling Price (SP) = $45
  • Loss = CP - SP = 50 - 45 = $5

Explanation:
The shopkeeper sold the shirt for $45, which is less than the cost price of $50. The loss is $5.

Example 3: Finding Profit Percentage

Question: A person buys a toy for $100 and sells it for $120. What is the profit percentage?

• Solution:
  • Cost Price (CP) = $100
  • Selling Price (SP) = $120
  • Profit = SP - CP = 120 - 100 = $20
  • Profit % = (Profit / CP) × 100 = (20 / 100) × 100 = 20%

Explanation:
The person made a profit of $20. Since the profit is 20% of the cost price, the profit percentage is 20%.

Example 4: Finding Loss Percentage

Question: A bicycle is bought for $200 and sold for $180. What is the loss percentage?

• Solution:
  • Cost Price (CP) = $200
  • Selling Price (SP) = $180
  • Loss = CP - SP = 200 - 180 = $20
  • Loss % = (Loss / CP) × 100 = (20 / 200) × 100 = 10%

Explanation:
The seller lost $20, which is 10% of the cost price. This means the loss percentage is 10%

Example 5: Finding Cost Price from Loss

Question: A chair is sold for $80 at a loss of $20. What is the cost price?

• Solution:
  • Selling Price (SP) = $80
  • Loss = $20
  • Cost Price (CP) = SP + Loss = 80 + 20 = $100

Explanation:
The chair was sold at a loss of $20, so the cost price was $100

Profit and Loss Percentage Formula

1. Profit Percentage Formula
   • Profit % = (Profit ÷ CP) × 100.
   • Example:
     If CP = $200 and Profit = $50,
     Profit % = (50 ÷ 200) × 100 = 25%.
2. Loss Percentage Formula
   • Loss % = (Loss ÷ CP) × 100.
   • Example:
     If CP = $300 and Loss = $60,
     Loss % = (60 ÷ 300) × 100 = 20%.
3. Selling Price with Profit or Loss
   • For Profit: SP = CP × (1 + Profit % / 100).
     Example:
     If CP = $100 and Profit % = 20%,
     SP = 100 × (1 + 20 / 100) = $120.

For Loss: SP = CP × (1 - Loss % / 100).
Example:
If CP = $200 and Loss % = 10%,
SP = 200 × (1 - 10 / 100) = $180.

Profit and Loss Tricks

Here are some easy tricks to solve profit and loss questions quickly:

1. Know the basic terms
   • Always remember these definitions:
     • Profit = Selling Price (SP) - Cost Price (CP).
     • Loss = Cost Price (CP) - Selling Price (SP).
2. Shortcut for Profit or Loss Percentage
   • Use these formulas:
     • Profit Percentage = (Profit ÷ Cost Price) × 100.
     • Loss Percentage = (Loss ÷ Cost Price) × 100.
3. Direct Selling Price Formula
   • To calculate SP directly:
     • If there is a profit: SP = CP × (1 + Profit % / 100).
     • If there is a loss: SP = CP × (1 - Loss % / 100).
4. Quick Cost Price Formula
   • To calculate CP directly:
     • If there is a profit: CP = SP ÷ (1 + Profit % / 100).
     • If there is a loss: CP = SP ÷ (1 - Loss % / 100).
5. Use approximate values
   • For faster calculations in exams, round off percentages or prices to simplify calculations.

Profit & Loss Assessment

1. A man buys a bag for $100 and sells it for $120. Find his profit and profit percentage.
2. A woman buys a dress for $200 and sells it for $180. Calculate her loss and loss percentage.
3. A shopkeeper buys 10 apples for $2 each and sells them for $25 in total. Did he make a profit or a loss? How much is it?
4. An artist sells a painting for $400, but it cost $350 to make. What is the profit and its percentage?

Take This Quiz :

Online Mock Test -3: Profit and Loss