Learning profit and loss is essential for anyone looking to excel in finance, business, or personal budgeting. Whether you’re preparing for competitive exams or aiming to boost your financial literacy, understanding profit and loss can give you a significant edge.

This guide will introduce you to effective profit and loss short tricks, profit loss percentage formulas, and practical methods to master these concepts. It also contains solved examples to help you understand and apply the concepts better. Discover how to learn profit and loss efficiently and accurately with our comprehensive guide.

Understanding Profit and Loss

What is Profit and Loss?

Profit and loss are fundamental concepts that reflect the financial health of any transaction or business operation. Here’s a quick breakdown:

Profit: When the selling price (SP) of an item is greater than its cost price (CP).

Profit=Selling Price−Cost Price

Loss: When the cost price (CP) of an item is greater than its selling price (SP).

Loss=Cost Price−Selling Price

The following image represents the basic formula required to learn Profit and Loss:

Profit and Loss Formulas

Profit & Loss Formula

Profit Calculation

Profit is calculated as the difference between the total revenue earned (income) and the total expenses incurred (costs).

Profit=Total Revenue−Total ExpensesProfit=Total Revenue−Total Expenses

Loss Calculation

Loss occurs when the total expenses exceed the total revenue.

Loss=Total Expenses−Total RevenueLoss=Total Expenses−Total Revenue

Profit and Loss Percentage Formula

To calculate the profit or loss percentage, use the following formulas:

• Profit Percentage: [Tex]\text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100[/Tex]
• Loss Percentage: [Tex]\text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100[/Tex]

Profit & Loss Key Components

• Total Revenue: This includes all income generated from sales, services, investments, etc.
• Total Expenses: This includes all costs incurred to generate revenue, such as production costs, operating expenses, taxes, etc.

Profit Margin

Profit Margin is a measure of profitability, represented as a percentage of revenue. It indicates how much profit a company makes for every dollar of revenue earned.

Profit Margin (%)=(ProfitTotal Revenue)×100Profit Margin (%)=(Total RevenueProfit​)×100

Gross Profit

Gross Profit is the profit earned after deducting the cost of goods sold (COGS) from total revenue.

Gross Profit=Total Revenue−Cost of Goods Sold (COGS)Gross Profit=Total Revenue−Cost of Goods Sold (COGS)

Net Profit

Net Profit is the profit remaining after deducting all expenses from revenue, including COGS, operating expenses, taxes, interest, etc.

Net Profit=Total Revenue – Total ExpensesNet Profit = Total Revenue – Total Expenses

Profit and Loss Short Tricks for Quick Calculations

Trick 1: Direct Percentage Calculation

If you need to quickly calculate the profit or loss percentage without going through intermediate steps, use this method:

• For Profit: [Tex]\text{Profit Percentage} = \left( \frac{\text{SP} – \text{CP}}{\text{CP}} \right) \times 100[/Tex]
• For Loss: [Tex]\text{Loss Percentage} = \left( \frac{\text{CP} – \text{SP}}{\text{CP}} \right) \times 100[/Tex]

Trick 2: Reverse Calculation

To find the cost price or selling price directly when the profit or loss percentage is known:

• Cost Price from Selling Price and Profit Percentage: [Tex]\text{CP} = \frac{\text{SP}}{1 + \left( \frac{\text{Profit Percentage}}{100} \right)}[/Tex]
• Selling Price from Cost Price and Profit Percentage: [Tex]\text{SP} = \text{CP} \times \left( 1 + \frac{\text{Profit Percentage}}{100} \right)[/Tex]

Related Articles:

• Profit & Loss
• Profit and Loss – Aptitude Questions and Answers
• Real-Life Applications of Profit and Loss

Solved Examples on Profit & Loss

Question 1: A shopkeeper sells a TV for $15,000 and makes a profit of 20%. What was the cost price of the TV?

Solution 1: Let the cost price of the TV be ????x.

Selling Price=Cost Price+ProfitSelling Price=Cost Price+Profit15000=????+0.2????15000=x+0.2x15000=1.2????15000=1.2x????=150001.2=12500x=1.215000​=12500

So, the cost price of the TV was $12,500.

Question 2: A book is sold for $180 at a loss of 10%. What was the cost price of the book?

Solution 2: Let the cost price of the book be ????x.

Selling Price=Cost Price−Loss Selling Price=Cost Price−Loss180=????−0.1????180=x−0.1x180=0.9????180=0.9x????=1800.9=200x=0.9180​=200

So, the cost price of the book was $200.

Question 3: A company sold 800 units of a product at $20 each. If the cost price per unit was $15, calculate the total profit or loss made.

Solution3:Total Revenue=800×20=16000Total Revenue=800×20=16000Total Cost=800×15=12000Total Cost=800×15=12000Profit=Total Revenue−Total CostProfit=Total Revenue−Total CostProfit=16000−12000=4000Profit=16000−12000=4000

So, the total profit made is $4,000.

Question 4: If a computer is sold for $900 at a loss of 10%, find its cost price.

Solution 4: Let the cost price of the computer be ????x.

Selling Price=Cost Price−LossSelling Price=Cost Price−Loss900=????−0.1????900=x−0.1x900=0.9????900=0.9x????=9000.9=1000x=0.9900​=1000

So, the cost price of the computer was $1,000.

Question 5: A trader marks his goods at 20% above cost price but allows a discount of 10% on the marked price. Find his gain or loss percent.

Solution 5: Let the cost price be ????x.

Marked Price=????+0.2????=1.2????Marked Price=x+0.2x=1.2xSelling Price=Marked Price−DiscountSelling Price=Marked Price−DiscountSelling Price=1.2????−0.1×1.2????=1.08????Selling Price=1.2x−0.1×1.2x=1.08xProfit=Selling Price−Cost PriceProfit=Selling Price−Cost PriceProfit=1.08????−????=0.08????Profit=1.08x−x=0.08x

Profit Percentage=(ProfitCost Price)×100Profit Percentage=(Cost PriceProfit​)×100Profit Percentage=(0.08????????)×100=8%Profit Percentage=(x0.08x​)×100=8%

So, the trader gains 8%.

Question 6: A car was bought for $20,000 and sold for $25,000. Calculate the profit percentage.

Solution 6:Cost Price=20000Cost Price=20000Selling Price=25000Selling Price=25000Profit=Selling Price−Cost Price=25000−20000=5000Profit=Selling Price−Cost Price=25000−20000=5000

Profit Percentage=(ProfitCost Price)×100Profit Percentage=(Cost PriceProfit​)×100Profit Percentage=(500020000)×100=25%Profit Percentage=(200005000​)×100=25%

So, the profit percentage is 25%.

Question 7: A trader sells an article at a loss of 10%. If the selling price is $450, find the cost price.

Solution 7: Let the cost price be ????x.

Selling Price=Cost Price−LossSelling Price=Cost Price−Loss450=????−0.1????450=x−0.1x450=0.9????450=0.9x????=4500.9=500x=0.9450​=500

So, the cost price is $500.

Question 8: A bike was sold at a profit of 25%. If the selling price was $2500, find the cost price.

Solution 8: Let the cost price be ????x.

Profit=Selling Price−Cost PriceProfit=Selling Price−Cost Price2500=????+0.25????2500=x+0.25x2500=1.25????2500=1.25x????=25001.25=2000x=1.252500​=2000

So, the cost price is $2000.

Question 9: If a shirt costing $400 is sold at a profit of 20%, find the selling price.

Solution 9: Let the cost price be $400.

Profit=0.2×400=80Profit=0.2×400=80Selling Price=Cost Price+Profit=400+80=480Selling Price=Cost Price+Profit=400+80=480

So, the selling price is $480.

Question 10: A shopkeeper sold a watch at a loss of 12%. If the selling price was $880, find the cost price.

Solution 10: Let the cost price be ????x.

Selling Price=Cost Price−LossSelling Price=Cost Price−Loss880=????−0.12????880=x−0.12x880=0.88????880=0.88x????=8800.88=1000x=0.88880​=1000

So, the cost price is $1000.

Practice Problems on Profit & Loss: Unsolved

Question 1: A retailer marks up the price of a product by 30% over its cost price. If the product was sold for $650, what was the cost price?

Question 2: A company bought 500 units of a product for $10 each. If 20% of the units were damaged and had to be sold at a 50% discount, and the remaining units were sold at a 25% profit, calculate the overall profit or loss made by the company.

Question 3: A trader buys 1000 oranges for $200 and sells them at a loss of 5%. What is the selling price per orange?

Question 4: An article was sold for $2250 at a loss of 10%. Find its cost price.

Question 5: If a bike is sold at a profit of 15% and the selling price is $3450, find the cost price.

Question 6: A shopkeeper sold 80% of his stock at a 25% profit and the remaining 20% at a 10% loss. If the total profit was $400, find the total cost price of the stock.

Question 7: A laptop was sold for $1800, resulting in a loss of 20%. Find the cost price of the laptop.

Question 8: A company sells its products at a 15% profit. If the cost price of a product is $80, what is its selling price?

Question 9: A shopkeeper marked the price of a chair 40% above its cost price. He then sold it at a 20% discount for $600. Find the cost price of the chair.

Question 10: A shopkeeper bought 200 pens for $400. If 20% of the pens were stolen and the remaining pens were sold at a 25% profit, calculate the overall profit or loss made by the shopkeeper.

Conclusion – How to Learn Profit & Loss

Mastering profit and loss calculations empowers individuals and businesses to make informed financial decisions. It ensures clarity on profitability, pricing strategies, and budgeting for sustainable growth.

How to Learn Profit & Loss- FAQs

What is the difference between profit and loss?

Profit is earned when revenue exceeds expenses, while loss occurs when expenses surpass revenue.

How is profit margin calculated?

Profit margin is calculated as (Profit / Total Revenue) * 100%. It indicates the percentage of profit earned per dollar of revenue.

What is gross profit?

Gross profit is revenue minus the cost of goods sold (COGS), representing the profit before deducting operating expenses.

How do you calculate net profit?

Net profit is total revenue minus total expenses, including COGS, operating costs, taxes, and interest.

Why is understanding profit and loss important for businesses?

It helps businesses evaluate financial health, set pricing strategies, forecast earnings, and make strategic decisions for growth and sustainability.