Basic Problems with Solutions – Profit and Loss

Let’s go through some basic profit and loss problems with detailed solutions.

We’ll break it down with definitions, formulas, and examples.

Definitions:

1. Profit: When the selling price of an item is higher than its cost price.
   Formula: Profit = Selling Price − Cost Price
2. Loss: When the selling price of an item is lower than its cost price.
   Formula: Loss = Cost Price − Selling Price
3. Profit Percentage: It is the percentage of profit on the cost price.
   Formula: Profit Percentage = (Profit/Cost Price) × 100
4. Loss Percentage: It is the percentage of loss on the cost price.
   Formula: Loss Percentage = (Loss/Cost Price)×100

Example Problems:

Example 1: Simple Profit Calculation

Problem: A book is purchased for $50 and sold for $70. What is the profit made?

Solution:

• Cost Price (CP) = $50
• Selling Price (SP) = $70

Profit = Selling Price − Cost Price = 70 − 50 = 20

Profit Made: $20

Example 2: Profit Percentage Calculation

Problem: A shirt is bought for $30 and sold for $45. Find the profit percentage.

Solution:

• Cost Price (CP) = $30
• Selling Price (SP) = $45

Profit = Selling Price − Cost Price = 45 − 30 = 15

Profit Percentage = (Profit/Cost Price) × 100

= (15/30) × 100 = 50%

Profit Percentage: 50%

Example 3: Simple Loss Calculation

Problem: A pen is purchased for $20 and sold for $15. What is the loss made?

Solution:

• Cost Price (CP) = $20
• Selling Price (SP) = $15

Loss = Cost Price − Selling Price

= 20 − 15 =5

Loss Made: $5

Example 4: Loss Percentage Calculation

Problem: A mobile phone is bought for $200 and sold for $180. Calculate the loss percentage.

Solution:

• Cost Price (CP) = $200
• Selling Price (SP) = $180

Loss = Cost Price − Selling Price

= 200 − 180

=20

Loss Percentage = (Loss/Cost Price) × 100

= (20/200) × 100

= 10%

Loss Percentage: 10%

Practice Problem:

Problem: A toy car is bought for $12 and sold for $15. Calculate the profit percentage.

Solution:

• Cost Price (CP) = $12
• Selling Price (SP) = $15

Profit = Selling Price − Cost Price

= 15 − 12

= 3

Profit Percentage = (Profit/Cost Price) × 100

= (3/12) × 100

= 25%

Profit Percentage: 25%

let’s break down the responses to problems involving profit and profit percentage with more detailed explanations and diagrams.

1: Simple Profit Calculation

Problem: A book is purchased for $50 and sold for $70. What is the profit made?

Solution:

1. Identify the Cost Price (CP): The amount paid to purchase the item. In this case, the Cost Price of the book is $50.
2. Identify the Selling Price (SP): The amount received from selling the item. In this case, the Selling Price of the book is $70.

Profit = Selling Price − Cost Price

Plugging in the values: Profit = 70 – 50

= 20

Conclusion: The profit made from selling the book is $20.

Diagram for Simple Profit Calculation:

CP     SP
  |      |
$50  -> $70
  \    /
  Profit
   $20

Profit Percentage Calculation

Problem: A shirt is bought for $30 and sold for $45. Find the profit percentage.

Solution:

1. Identify the Cost Price (CP): The amount paid to purchase the item. In this case, the Cost Price of the shirt is $30.
2. Identify the Selling Price (SP): The amount received from selling the item. In this case, the Selling Price of the shirt is $45.
3. Calculate the Profit: The difference between the Selling Price and the Cost Price.

Profit = Selling Price − Cost Price

= 45 − 30

= 15

4. Calculate the Profit Percentage: The profit as a percentage of the Cost Price.

Profit Percentage = (Profit/Cost Price) × 100

Plugging in the values: Profit Percentage = (15/30) × 100

= 50%

Conclusion: The profit percentage from selling the shirt is 50%.

Diagram for Profit Percentage Calculation:

CP     SP
  |      |
$30  -> $45
  \    /
  Profit
   $15

Profit Percentage Calculation:
  Profit        CP
    |           |
   $15  /  $30  -> 0.5  -> 0.5 * 100 = 50%
  \        /
  Profit Percentage
    50%

Additional Example:

Example: Profit and Profit Percentage Calculation

Problem: A toy car is bought for $10 and sold for $15. Calculate the profit and the profit percentage.

Solution:

1. Identify the Cost Price (CP): The amount paid to purchase the toy car. In this case, it is $10.
2. Identify the Selling Price (SP): The amount received from selling the toy car. In this case, it is $15.
3. Calculate the Profit:

Profit = Selling Price − Cost Price

= 15−10

= 5

4. Calculate the Profit Percentage:

Profit Percentage = (Profit/Cost Price) × 100

= (5/10)×100

= 50%

Conclusion: The profit made from selling the toy car is $5, and the profit percentage is 50%.

Diagram for Toy Car Example:

  CP     SP
  |      |
$10  -> $15
  \    /
  Profit
   $5
Profit Percentage Calculation:
  Profit        CP
    |           |
   $5  /  $10  -> 0.5  -> 0.5 * 100 = 50%
  \        /
  Profit Percentage
    50%

Problem 1: Calculating Profit and Profit Percentage

Question: John bought a bicycle for $200 and sold it for $250. Calculate the profit and the profit percentage.

Solution:

1. Profit Calculation: Profit = Selling Price (SP)− Cost Price (CP)
2. Profit = 250 − 200 = 50
3. Profit Percentage Calculation:
4. Profit Percentage = (Profit/Cost Price (CP)) × 100
5. Profit Percentage = (50/200) × 100 = 25%

Answer: Profit = $50, Profit Percentage = 25%

Problem 2: Calculating Loss and Loss Percentage

Question: Alice bought a camera for $500 and sold it for $450. Calculate the loss and the loss percentage.

Solution:

1. Loss Calculation: Loss = Cost Price (CP)−Selling Price (SP)
2. Loss = 500 − 450 = 50
3. Loss Percentage Calculation: Loss Percentage=(Loss/Cost Price (CP)) × 100
4. Loss Percentage = (50/500​) × 100 = 10%

Answer: Loss = $50, Loss Percentage = 10%

Problem 3: Determining Selling Price for Desired Profit Percentage

Question: David wants to sell a laptop for a profit of 20%. If the cost price of the laptop is $800, at what price should he sell it?

Solution:

1. Selling Price Calculation: Selling Price (SP)=Cost Price (CP)+ Profit
2. Profit = (Desired Profit Percentage/100)×Cost Price (CP)
3. Profit = (20/100) × 800 = 160
4. Selling Price (SP) = 800 + 160 = 960

Answer: Selling Price = $960

Problem 4: Finding Cost Price from Selling Price and Profit Percentage

Question: Emma sold a painting for $1200, making a profit of 25%. What was the cost price of the painting?

Solution:

1. Cost Price Calculation: Profit Percentage={(Selling Price (SP)− Cost Price (CP)}/Cost Price (CP)) × 100
2. Rearrange to find CP: Selling Price (SP) = Cost Price (CP) × {(1+Profit Percentage)/100)}
3. 1200 = CP × (1+25/100​)
4. 1200 = CP × 1.25
5. CP = 1200/1.25 = 960

Answer: Cost Price = $960

Problem 5: Determining Selling Price for Desired Loss Percentage

Question: Michael bought a watch for $150. He wants to sell it at a loss of 10%. At what price should he sell it?

Solution:

1. Selling Price Calculation: Selling Price (SP) = Cost Price (CP) − Loss
2. Loss = {(Desired Loss Percentage/100)} × Cost Price (CP)
3. Loss = (10/100) × 150 = 15
4. Selling Price (SP) = 150 − 15 = 135

Answer: Selling Price = $135