What is Profit and Loss? Describe with the help of an example

Imagine you buy a cool gaming notebook for $20 and later sell it to your friend for $25. You made an extra $5. That extra money is called Profit. But what if you had to sell it for $15 because it was slightly used? You would lose $5, which is called a Loss.

In the world of business, commerce, and everyday shopping, understanding cost price and selling price is one of the most practical life skills you can learn. It helps you manage pocket money, understand how stores price items during sales, and build a strong foundation for financial literacy.

In mathematics, profit and loss refer to the financial outcomes of business transactions or investments. They are fundamental concepts in finance and accounting, providing insight into the success or failure of ventures. Let's delve deeper into each concept.

Meet the Key Players: Basic Terminology :-

Before we dive into any profit and loss formula, let’s meet the four main characters in our story:

Cost Price (CP): The amount of money you pay to buy an article or produce it.
Selling Price :- The amount of money you receive when you sell that article.
Profit (or Gain): When you sell an item for more than what you bought it for.
$\text{Profit} = \text{Selling Price (SP)} - \text{Cost Price (CP)}$
(Condition: $\text{SP} > \text{CP}$ )
Loss: When you sell an item for less than what you bought it for.
$\text{Loss} = \text{Cost Price (CP)} - \text{Selling Price (SP)}$
(Condition: $\text{CP} > \text{SP}$ )

Golden Rule: Profit and Loss are always calculated on the Cost Price (CP) unless specified otherwise in the question!

A) Profit:

Profit is the financial gain realized when the revenue generated from selling goods or services exceeds the total expenses incurred in producing or acquiring those goods or services. It represents the positive difference between income and expenditure.

Example of Profit:

Suppose you run a lemonade stand. Your total revenue from selling lemonade for a day is $100. However, you had to spend $60 on ingredients (lemons, sugar, water) and other expenses (cups, signage). To calculate your profit, you subtract your expenses from your revenue:

Profit = Revenue - Expenses Profit = $100 - $60 Profit = $40

In this example, your profit from the day's sales is $40.

Visual & Graphical Representation of Profit and Loss :-

Scenario A: The Profit Journey

[ YOU BUY ] ---> [ YOU SELL ] Cost Price (CP) Selling Price (SP) $50 $70 | | +--------------> [ +$20 ] ------------+ PROFIT!

Scenario B: The Loss Journey

[ YOU BUY ] ---> [ YOU SELL ] Cost Price (CP) Selling Price (SP) $100 $70 | | +--------------> [ -$30 ] ------------+ Loss!

Types of Profit:

1. Gross Profit:

- Calculation: Gross Profit = Revenue - Cost of Goods Sold (COGS)

- Description: Represents the profit a company makes from its core business activities before subtracting operating expenses, interest, and taxes. It shows how efficiently a company produces and sells its products.

2. Operating Profit (or Operating Income):

- Calculation: Operating Profit = Gross Profit - Operating Expenses (e.g., rent, salaries, utilities)

- Description: Reflects the profit from regular business operations, excluding non-operating income and expenses (like interest and taxes). It indicates the effectiveness of a company’s core business operations.

3. Net Profit (or Net Income):

- Calculation: Net Profit = Operating Profit - Non-Operating Expenses (e.g., interest, taxes) + Non-Operating Income

- Description: The final profit after all expenses, including operating expenses, interest, taxes, and any other non-operating income or expenses, have been deducted. It represents the overall profitability of the business.

Significance:

- Indicator of Success: Positive profit indicates that the business is generating more revenue than its costs, which is a sign of financial health.

- Investment Decisions: Investors often look at profit margins to evaluate the attractiveness of a business.

- Business Growth: Profits can be reinvested into the business to fund expansion or innovation.

B) Loss:

Loss, on the other hand, occurs when the expenses incurred exceed the revenue generated. It represents a negative difference between income and expenditure, indicating that the business or investment did not generate enough revenue to cover its costs.

Example of Loss:

Continuing with the lemonade stand example, let's say that on a rainy day, you only manage to sell $30 worth of lemonade. However, your expenses remain the same at $60. To calculate your loss, you subtract your revenue from your expenses:

Loss = Revenue - Expenses Loss = $30 - $60 Loss = -$30

In this scenario, your loss from the day's sales is $30. The negative sign indicates that your expenses exceeded your revenue, resulting in a loss.

Types of Loss:

1. Gross Loss:

- Calculation: Gross Loss = Cost of Goods Sold - Revenue (when COGS exceeds revenue)

- Description: Represents a situation where the cost of producing goods or services exceeds the revenue generated from their sale. This is an initial indicator that the core business activities are unprofitable.

2. Operating Loss:

- Calculation: Operating Loss = Operating Expenses - Gross Profit (when operating expenses exceed gross profit)

- Description: Occurs when a business's operating expenses surpass the gross profit. It suggests that the business is not managing its operating costs effectively relative to its revenue.

3. Net Loss:

- Calculation: Net Loss = Total Expenses - Total Revenue (when total expenses exceed total revenue)

-Description: The final loss after accounting for all expenses, including operating costs, interest, taxes, and any other non-operating costs. It reflects the overall financial performance of the business.

Significance:

- Indicator of Financial Trouble: Persistent losses can indicate financial instability and potential trouble in sustaining business operations.

- Decision-Making: Losses can prompt management to review and adjust business strategies, reduce costs, or explore new revenue streams.

- Impact on Stakeholders: Continuous losses can affect investor confidence and potentially lead to financial restructuring or closure.

The Magic Formulas & Shortcuts

To solve any problem quickly, you need the right tools. Here is your cheat sheet for all essential profit and loss formulas:

Basic Formulas

Profit = $\text{SP} - \text{CP}$

Loss = $\text{CP} - \text{SP}$

Profit Percentage ( $\text{Profit}\%$ ) =

\left(\frac{\text{Profit}}{\text{CP}}\right) \times 100

Loss Percentage ( $\text{Loss}\%$ ) =

\left(\frac{\text{Loss}}{\text{CP}}\right) \times 100

Direct Formula Shortcuts

Sometimes questions give you the Cost Price and Profit/Loss Percentage, and you need to find the Selling Price directly:

When there is a Profit%:
$\text{SP} = \text{CP} \times \left(\frac{100 + \text{Profit}\%}{100}\right)$
When there is a Loss%:
$\text{SP} = \text{CP} \times \left(\frac{100 - \text{Loss}\%}{100}\right)$

Conversely, if you know the Selling Price and want to find the Cost Price:

From a Profit%:
$\text{CP} = \text{SP} \times \left(\frac{100}{100 + \text{Profit}\%}\right)$
From a Loss%:
CP = SP * (100)/(100 - Loss%)

Step-by-Step Solved Examples

Let's practice applying these formulas through real-world word problems.

Example 1: Finding Profit and Profit Percentage

Problem: Alex buys a bicycle for $150. After using it for a year, he sells it to his neighbour for $180. Find Alex's profit and profit percentage.

Step 1: Identify the given values. Cost Price (CP) = $150

Selling Price (SP) = $180

Step 2: Check whether it's a profit or loss.
Since $\text{SP} > \text{CP}$ ( $\$180 > \$150$ ), Alex made a Profit.
Step 3: Calculate Profit.
$\text{Profit} = \text{SP} - \text{CP} = 180 - 150 = \$30$
Step 4: Calculate Profit Percentage.
$\text{Profit}\% = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100$
$\text{Profit}\% = \left(\frac{30}{150}\right) \times 100 = \left(\frac{1}{5}\right) \times 100 = 20\%$

Answer: Alex made a profit of $30, which is a 20% profit.

Example 2: Finding Selling Price from Cost Price and Loss Percentage

Problem: A shopkeeper buys a smartphone for $400. Due to a new model release, he has to sell it at a 15% loss. What is the selling price of the smartphone?

Step 1: Identify given values.
- $\text{CP} = \$400$
- $\text{Loss}\% = 15\%$
Step 2: Apply the direct shortcut formula for loss.
$\text{SP} = \text{CP} \times \left(\frac{100 - \text{Loss}\%}{100}\right)$
$\text{SP} = 400 \times \left(\frac{100 - 15}{100}\right)$
$\text{SP} = 400 \times \left(\frac{85}{100}\right)$
Step 3: Simplify and calculate.
$\text{SP} = 4 \times 85 = \$340$

Answer: The selling price of the smartphone is $340.

Advanced Concepts: Marked Price (MP) and Discounts

When you go to a shopping mall, you rarely buy items at their original price tag. This brings us to three new terms:

Marked Price (MP) / List Price: The price printed on the label or price tag.
Discount: A reduction offered by the shopkeeper on the Marked Price.
Selling Price (SP): The final price after the discount is subtracted from the Marked Price.

Discount = Marked Price (MP) - Selling Price (SP)
Discount % = (Discount /Marked Price) * 100
SP = MP - Discount
Finding Selling Price with Discount

Problem: A jacket has a marked price of $80. The store offers a 25% discount during a clearance sale. Find the selling price of the jacket.

Discount Amount = $25\%$ of $\$80$ = $\frac{25}{100} \times 80 = \$20$
Selling Price = $\text{MP} - \text{Discount} = \$80 - \$20 = \$60$
Answer: You can buy the jacket for $60.

Q1) A shopkeeper gives discount of 25% on a toy and still makes a profit of 20%., He gain Rs.360 then find marked price of toy.

Let find the cost price of the toy

So the formula of the cost price will be

CP = profit /profit% * 100

= 360/20*100

= Rs. 1800

Now

SP = (100+profit % / 100 )* cp

=( 100+20/100)*1800

= (120/100)*1800

=Rs. 2160

Now

Marked Price = (100/100-discount%)*SP

= (100/100-25)*2160

= 100/75*2160

= Rs 2880

Q2 Raju bought a music instrument for ₹9260 and spent ₹850 on repairs. She sold it at a profit of ₹910. What is the Selling Price (SP)?

Solution :- Cost Price for Music Instrument = ₹9260

Cost Spend on its repairing = ₹850

Total CP = ₹9260 + ₹850 = ₹10,110

We know,

Profit = SP - CP

Then

SP = CP+ Profit

= ₹10,110 + ₹910

= ₹11,020

Self-Assessment Practice Quiz

Test your understanding! Try solving these 10 questions on your own before checking the answer key at the bottom.

If an article is bought for $250 and sold for $300, find the profit percentage.
- A) 10%
- B) 15%
- C) 20%
- D) 25%
A man sells a watch for $450 at a loss of 10%. Find the cost price of the watch.
- A) $400
- B) $500
- C) $495
- D) $480
By selling a book for $72, a vendor loses 10%. To gain 10%, what should be the selling price?
- A) $80
- B) $88
- C) $90
- D) $96
The cost price of 12 pens is equal to the selling price of 10 pens. Find the profit percentage.
- A) 10%
- B) 15%
- C) 20%
- D) 25%
An item marked at $200 is sold for $160. What is the percentage of discount given?
- A) 15%
- B) 20%
- C) 25%
- D) 30%
If the cost price of an article is 80% of its selling price, then the profit percentage is:
- A) 20%
- B) 25%
- C) 30%
- D) 40%
A trader marks his goods 20% above the cost price and allows a 10% discount on the marked price. What is his net profit percentage?
- A) 8%
- B) 10%
- C) 12%
- D) 15%
If a shirt is sold at a 12% profit instead of an 8% loss, the seller gets $40 more. Find the cost price of the shirt.
- A) $350
- B) $400
- C) $450
- D) $500
Successive discounts of 20% and 10% are equivalent to a single discount of:
- A) 28%
- B) 30%
- C) 25%
- D) 26%
A dishonest dealer professes to sell his goods at cost price, but uses a false weight of 900 grams instead of 1 kilogram. What is his actual profit percentage?
- A) 10%
- B) $11 \frac{1}{9}\%$
- C) $12 \frac{1}{2}\%$
- D) 15%

Global-Level Quiz Competition Questions

International math competitions, Olympiads, and AMC (American Mathematics Competitions) love testing deeper logical reasoning using profit and loss frameworks. Let's look at 3 advanced competition-level problems with complete step-by-step solutions.

Competition Question 1: The Mixed Fruit Stand (AMC Style)

Problem:

A fruit vendor buys equal numbers of apples and oranges. He sells apples at a profit of 25% and oranges at a loss of 10%. If he sells a total of 100 fruits and his overall profit is 10%, how many apples did he sell?

Solution Strategy:

Let the cost price of 1 apple be $C$ and 1 orange be $C$ (since he buys equal numbers of each, we can assume unit cost prices are equal or use proportions). Let the number of apples be $x$ , and therefore the number of oranges is also $x$ (equal numbers).
Profit on apples = 25%. Selling price of 1 apple = $1.25C$ .
Loss on oranges = 10%. Selling price of 1 orange = $0.90C$ .
Total CP for $x$ apples and $x$ oranges = $x \cdot C + x \cdot C = 2xC$ .
Total SP = $1.25Cx + 0.90Cx = 2.15Cx$ .
Overall profit is given as 10%.
$\text{Total SP} = \text{Total CP} \times 1.10 = 2xC \times 1.10 = 2.20Cx$
Wait, let's re-verify the overall profit condition.
If total fruits = 100, and equal numbers of apples and oranges are bought, then $x = 50$ apples and $50$ oranges.
Let's check the aggregate profit percentage formula:
$\text{Overall Profit}\% = \frac{\text{Profit}_{\text{apples}} + \text{Profit}_{\text{oranges}}}{\text{Total CP}} \times 100$
- Profit on 50 apples at 25% each = $50 \times 0.25C = 12.5C$
- Loss on 50 oranges at 10% each = $50 \times (-0.10C) = -5C$
- Net Profit = $12.5C - 5C = 7.5C$
- Total CP for 100 fruits = $100C$
- Overall Profit Percentage = ( $\frac{7.5C}{100C} \times 100 = 7.5\%$
Wait, the question states overall profit is 10%. Let's set up the exact ratio of apples to oranges if the quantities can vary, or re-evaluate the ratio equation.
Let the number of apples be $a$ and oranges be $b$ .
Profit from apples = $0.25 \times (\text{CP of apples})$
Loss from oranges = $0.10 \times (\text{CP of oranges})$
Let $\text{CP of each fruit be equal}$ .
Total Profit = $0.25a - 0.10b$
Total CP = $a + b$
Given overall profit = 10% = $0.10$ .
$\frac{0.25a - 0.10b}{a + b} = 0.10$
$0.25a - 0.10b = 0.10a + 0.10b$
$0.25a - 0.10a = 0.10b + 0.10b$
$0.15a = 0.20b$
$\frac{a}{b} = \frac{0.20}{0.15} = \frac{4}{3}$
Since total fruits = 100, and $a + b = 100$ :
$4k + 3k = 100 \implies 7k = 100$ (Let's adjust numbers or check total fruits).
Let's assume the question meant total ratio splits neatly or let's use a cleaner problem format for competition standard:

Revised Clean Competition Problem:

A merchant buys two types of rice at $40 per kg and $60 per kg. In what ratio must he mix them so that by selling the mixture at $55 per kg, he makes a 10% profit?

Solution:

Find the Cost Price of the Mixture:
Selling Price of mixture $\text{SP}$ = $55 per kg.
Profit = 10%.
$\text{CP of mixture} = \text{SP} \times \left(\frac{100}{100 + \text{Profit}\%}\right)$
$\text{CP of mixture} = 55 \times \left(\frac{100}{110}\right) = 55 \times \frac{10}{11} = \$50\text{ per kg}$
Apply Alligation Rule (Weighted Averages):
- Cost of Type 1 Rice = $40
- Cost of Type 2 Rice = $60
- Mean Cost = $50
$\text{Ratio} = \frac{\text{Cost of Type 2} - \text{Mean Cost}}{\text{Mean Cost} - \text{Cost of Type 1}} = \frac{60 - 50}{50 - 40} = \frac{10}{10} = 1:1$

Answer: He must mix the two types of rice in a 1:1 ratio.

Competition Question 2: Successive Discounts & Markup (Olympiad Level)

Problem:

A trader marks up his goods by $60\%$ above the cost price. He then gives a succession of two discounts: $20\%$ and $x\%$ . If his net profit is $12\%$ , find the value of $x$ .

Solution:

Let the Cost Price $\text{CP}$ = $\$100$ .
Since the goods are marked up by $60\%$ :
$\text{Marked Price (MP)} = 100 + 60\% \text{ of } 100 = \$160$
Net profit is $12\%$ , which means the final Selling Price $\text{SP}$ is:
$\text{SP} = 100 + 12\% \text{ of } 100 = \$112$
The Marked Price is $\$160$ , and after two successive discounts $20\%$ and $x\%$ , the final Selling Price is $\$112$ .
- First discount = $20\%$ on $\$160$ :
  $\text{Price after 1st discount} = 160 \times \left(1 - \frac{20}{100}\right) = 160 \times 0.80 = \$128$
Now, the second discount of $x\%$ is applied on $\$128$ to reach the final $\text{SP}$ of $\$112$ :
$128 \times \left(1 - \frac{x}{100}\right) = 112$
$1 - \frac{x}{100} = \frac{112}{128}$
Simplify the fraction $\frac{112}{128}$ by dividing by 16:
$\frac{112}{128} = \frac{7}{8} = 0.875$
$1 - \frac{x}{100} = 0.875$
$\frac{x}{100} = 1 - 0.875 = 0.125$
$x = 0.125 \times 100 = 12.5$

Answer: The second discount percentage x is 12.5%.

9. Answer Key for Self-Assessment Quiz

C (20%) — $\text{Profit} = 300 - 250 = 50$ . $\text{Profit}\% = (50 / 250) \times 100 = 20\%$ .
B ($500) — $\text{CP} = \text{SP} \times \left(\frac{100}{100 - 10}\right) = 450 \times \frac{100}{90} = 500$ .
B ($88) — $\text{CP} = 72 \times \frac{100}{90} = 80$ . New $\text{SP}$ for $10\%$ profit $= 80 \times 1.10 = 88$ .
C (20%) — Let CP of 1 pen = $1. Total CP of 10 pens = $10 = SP of 10 pens. Profit on 10 pens = $12 - 10 = 2$ . Profit $\% = (2 / 10) \times 100 = 20\%$ .
B (20%) — $\text{Discount} = 200 - 160 = 40$ . Discount $\% = (40 / 200) \times 100 = 20\%$ .
B (25%) — Let $\text{SP} = 100$ , then $\text{CP} = 80$ . Profit $= 20$ . Profit $\% = (20 / 80) \times 100 = 25\%$ .
A (8%) — Let $\text{CP} = 100, \text{MP} = 120$ . $\text{SP} = 120 \times 0.90 = 108$ . Profit $= 8\%$ .
B ($400) — Difference in percentages % $= 12\% - (-8\%) = 20\%$ . $20\% \text{ of CP} = 40 \implies \text{CP} = \$400$ .
A (28%) — Effective discount formula: $A + B - \frac{A \times B}{100} = 20 + 10 - \frac{200}{100} = 30 - 2 = 28\%$ .
B ( $11 \frac{1}{9}\%$ ) — Profit $\% = \left(\frac{\text{Error}}{\text{True Value} - \text{Error}}\right) \times 100 = \left(\frac{100}{1000 - 100}\right) \times 100 = \frac{100}{900} \times 100 = 11.11\%$ or $11 \frac{1}{9}\%$ .

What is Profit and Loss? Describe with example

What is Profit and Loss? Describe with the help of an example

Meet the Key Players: Basic Terminology :-

A) Profit:

Visual & Graphical Representation of Profit and Loss :-

Scenario B: The Loss Journey

[ YOU BUY ] ---> [ YOU SELL ] Cost Price (CP) Selling Price (SP) $100 $70 | | +--------------> [ -$30 ] ------------+ Loss!

Types of Profit:

1. Gross Profit:

B) Loss:

Basic Formulas

Profit = $\text{SP} - \text{CP}$

Loss = $\text{CP} - \text{SP}$

Direct Formula Shortcuts

Step-by-Step Solved Examples

Example 1: Finding Profit and Profit Percentage

Example 2: Finding Selling Price from Cost Price and Loss Percentage

Advanced Concepts: Marked Price (MP) and Discounts

Self-Assessment Practice Quiz

Global-Level Quiz Competition Questions

Competition Question 1: The Mixed Fruit Stand (AMC Style)

Solution Strategy:

Solution:

Competition Question 2: Successive Discounts & Markup (Olympiad Level)

Solution:

9. Answer Key for Self-Assessment Quiz

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What is Profit and Loss? Describe with example

What is Profit and Loss? Describe with the help of an example

Meet the Key Players: Basic Terminology :-

A) Profit:

Visual & Graphical Representation of Profit and Loss :-

Scenario B: The Loss Journey[ YOU BUY ] ---> [ YOU SELL ] Cost Price (CP) Selling Price (SP) $100 $70 | | +--------------> [ -$30 ] ------------+ Loss!

Types of Profit:

1. Gross Profit:

B) Loss:

Basic Formulas

Profit = SP - CP

Loss = CP - SP

Direct Formula Shortcuts

Step-by-Step Solved Examples

Example 1: Finding Profit and Profit Percentage

Example 2: Finding Selling Price from Cost Price and Loss Percentage

Advanced Concepts: Marked Price (MP) and Discounts

Self-Assessment Practice Quiz

Global-Level Quiz Competition Questions

Competition Question 1: The Mixed Fruit Stand (AMC Style)

Solution Strategy:

Solution:

Competition Question 2: Successive Discounts & Markup (Olympiad Level)

Solution:

9. Answer Key for Self-Assessment Quiz

Post a Comment

Contact Form

Scenario B: The Loss Journey

[ YOU BUY ] ---> [ YOU SELL ] Cost Price (CP) Selling Price (SP) $100 $70 | | +--------------> [ -$30 ] ------------+ Loss!

Profit = $\text{SP} - \text{CP}$

Loss = $\text{CP} - \text{SP}$