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Profit and Loss

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Introduction to Profit and Loss with Formulas

In general words, Profit and Loss are more than just numbers—it's like a game where you measure how well you’ve done in a deal! Counting your profit feels rewarding, like finding extra money in your pocket, while understanding your loss teaches valuable lessons. Let’s look into the basics and make solving these problems a fun experience!


Every company and business works on the fundamental concept of profit and loss. It is very important to familiarize yourself with profit and loss, not only to run a business or company but also to keep an account of your own expenditure. Money is actually a tricky concept to explain to kids without giving them an opportunity to get hands-on experience. Parents often take their kids to the supermarket to make them learn about the price marked on every good and the calculation of total price. Later, kids come across the concept of discount on the cost price and the concept of comparing prices before purchasing. Comparing prices is also a form of profit and loss as you learn to save money by buying the same good at a comparatively lesser price. 

 

The term 'Profit and Loss' is a concept developed from various applications to real-life problems which take place in our lives almost every day. When a good is re-purchased at a greater price then a profit is incurred. Similarly, if the good is repurchased at a lesser price then there is a loss. 

 

Terms related to Profit and Loss

We have come across the word profit and loss many times. Profit stands for gain, advantage or benefit whereas loss is the opposite of profit that involves expenditure as compared to gain.

Cost Price (CP):  Cost Price is the amount at which a product is purchased. Sometimes it also includes overhead expenses, transportation cost, etc. For example, you bought a refrigerator at Rs 10,000 and spent Rs 2000 for transportation and Rs 500 for set up. So the total cost price is the sum of all the expenditure done, that is, Rs 12,500.

Selling Price (SP):  Selling Price is the amount at which a product is sold. It may be more than, equal to or less than the cost price of the product. For example, if a shopkeeper bought a chair at Rs 500 and sold it at Rs 600, then the cost price of the chair is Rs 500 and the selling price of the chair is Rs 600. 

Discount: A discount is the amount by which the original price of something is reduced. It’s like getting a special price or a deal, so you pay less than the actual price.

Profit (P): If a product is sold at a price more than its cost price then the seller makes a profit. For example, a plot was purchased at Rs 50,000 and three years later it was sold at Rs 1,50,000 then there is a profit of 1 lakh. 

Loss (L): If a product is sold at a price less than its cost price then the seller makes a loss. 

For example, a phone is bought at Rs 20,000 and a year later it was sold for Rs 12,000 then the seller made a loss of Rs 8000.

Profit Percent (P%): It is the percentage of profit on the cost price. 

Loss Percent (L%): It is the percentage of loss on the cost price.


Concept of Profit and Loss

Let us understand the concept in a simpler way by using profit and loss Math. Suppose a shopkeeper buys a pen at Rs 8 from the market and sells it at Rs 10 at his shop.

Amount invested by the shopkeeper or Cost Price = Rs 8

The amount received by the shopkeeper or Selling Price = Rs 10

Rule 1

If the cost is less than the Selling price then it’s a profit. 

CP < SP ------ Profit

If the cost price is more than Selling Price then it’s a loss.

CP > SP  ------ Loss


In the above example, the selling price is more than the cost price so that means the shopkeeper made a profit. 

Rule 2

To find the amount of profit or loss, subtract the smaller value from greater value.

In the case of profit, the selling price is always more than the cost price. 

Profit = Selling Price - Cost Price.

Similarly, in the case of loss, the cost price is more than the selling price.

Loss = Cost Price - Selling Price.


Here, 

Cost Price = Rs 8

Selling Price = Rs 10

Profit = Selling Price - Cost Price

         =  Rs 10 - Rs 8

         = Rs 2

Therefore, the shopkeeper made a profit of Rs 2 on selling a pen.

Now, let us find what percent of profit was made by the shopkeeper.


Rule 3:

In order to find the percentage, we divide the term we are finding the percentage of by total amount and then multiply the resultant with 100.

 

Profit % = \[\dfrac{{profit}}{{{\text{Cost Price}}}} \times \] 100

Loss % =\[\dfrac{{Loss}}{{{\text{Cost price}}}} \times \] 100


Here, 

Profit % =\[\dfrac{{profit}}{{\operatorname{Cos} t{\text{ }}price}} \times 100\]

             =  \[\dfrac{2}{{10}} \times 100\]

             = 20%

 

Thus, the shopkeeper made a profit of 20% of the cost price.


Profit and Loss Percentage Formula

Given below are profit and loss formula and tricks to derive the value of other terms from the basic fundamental formulas:

  Profit

Loss

CP < SP

Profit = Selling Price - Cost Price

Selling Price = Cost Price + Profit

Cost Price = Selling price - Profit

Profit % =\[\dfrac{{profit}}{{\operatorname{Cos} t{\text{ }}price}}\]\[ \times \]100

Cost Price =\[\dfrac{{profit}}{{profit{\text{ }}\% }}\]\[ \times \] 100

Profit = \[\dfrac{{profit}}{{100}} \times \] Cost Price

CP > SP 

Loss = Cost Price - Selling Price

Cost Price = Selling Price + Loss

Selling Price = Cost Price - Loss

Loss % =\[\dfrac{{Loss}}{{{\text{Cost price}}}} \times \] 100

Loss  = \[\dfrac{{Loss\% }}{{100}}\]\[ \times \] Cost Price

Cost Price = \[\dfrac{{Loss}}{{{\text{Loss }}\% }}\]\[ \times \] 100


Solved Examples on How to Calculate Profit and Loss:

Given below are the profit and loss examples found in real life:

  1. Find the Selling price of a bicycle of Rs 700 if

  1. Loss is Rs 50 

  2. If Profit percentage is 50%

Solution:  

  1. CP = Rs 700

Loss = Rs 50

Let SP be x.

We know in case of loss, the cost price is more than the selling price. 

By using the formula of CP and SP.

Loss = CP - SP

Rs 50 = Rs 700 - x

x = Rs 700 - Rs 50

x = Rs 650

Thus, the selling price is Rs 650.

 

  1. CP = Rs 700

            Profit % = 50

            Let the profit be x.


Profit % = \[\dfrac{{profit}}{{\operatorname{Cos} t{\text{ }}price}}\]\[ \times \] 100

50 = \[\dfrac{x}{{700}} \times 100\]

\[50 = \dfrac{x}{7}\]

x = 7\[ \times \]50

x = Rs 350


Profit = Rs 350.

From the profit and loss Mathematics formula, 

Profit = SP - CP

Rs 350 = SP - Rs 700

SP = Rs 700 + Rs 350

      = Rs 1050

Thus, the selling price is Rs 1050 if the profit is 50% of the cost price.


2) A shopkeeper bought two TV sets at Rs 10,000 each such that he can sell one at a profit of 10% and the other at a loss of 10%. Find his overall profit or loss.

Solution:

The shopkeeper bought two TV sets. He made a profit by selling one and a loss by selling another. So let us divide the solution into two parts:

The cost price of TV = Rs 10,000  

Profit % = 10 % of cost price

According to the formula,

Profit % = \[\dfrac{{profit}}{{\operatorname{Cos} t{\text{ }}price}} \times 100\]

\[10 = \dfrac{{profit}}{{10,000}} \times 100\]

\[10 = \dfrac{{profit}}{{100}}\]

 

Therefore, Profit = Rs 1000

If CP = Rs 10,000 and Profit = Rs 1000

Then, SP = 10,000+1000 = Rs 11000

The cost price of TV = Rs 10,000  

Loss % = 10 % of cost price

According to the formula,

Loss % = \[\dfrac{{Loss}}{{\operatorname{Cos} t{\text{ }}price}} \times 100\]

\[10 = \dfrac{{Loss}}{{10,000}} \times 100\]

\[10 = \dfrac{{Loss}}{{100}}\]

 

Therefore, Loss = Rs 1000

If CP = Rs 10,000 and Loss = Rs 1000

Then, SP = 10,000-1000 = Rs 9000

 

                                                                            

Total Cost price = Rs 10,000 + Rs 10,000

                          = Rs 20,000

Total Selling price = Rs 11,000 + Rs 9000

                              = Rs 20,000

As the cost price is equal to the loss price, there is neither a profit nor a loss.

 

3) A shopkeeper bought 200 bulbs for Rs 10 each. Out of those, 5 bulbs were fused so he sold the remaining at Rs 12 each. Find the percentage of gain or loss. 

Solution:

No of bulbs shopkeeper bought = 200

Cost of 1 bulb = Rs 10

Cost of 200 bulbs = Rs 10 x 200 = Rs 2000.

Therefore, the total cost price of 200 bulbs is Rs 2000

If 5 bulbs are thrown away then the number of bulbs left = 200 - 5 = 195.

Selling price of one bulb = Rs 12

Selling price of 195 bulbs = Rs 195 x 12 = Rs 2340

Therefore, the total selling price of 200 bulbs is Rs 2340

Selling price is more than the cost price, this means that the shopkeeper made a profit.

Profit = SP - CP

         = Rs 340


Profit % =\[\dfrac{{profit}}{{\operatorname{Cos} t{\text{ }}price}} \times 100\]

              = \[\dfrac{{340}}{{2000}} \times 100\]

              = 17%


Thus, the shopkeeper made a profit of 17% on selling 195 bulbs at Rs 12.

 

4) Ankit bought a plot at Rs 2,25,000. He wanted an overall profit of 12% but he sold one-third of the plot at a loss of 8% so at what price should he sell the remaining plot of land? 

Solution:

The cost price of the entire plot = Rs 2,25,000. 

 

Cost price of 1/3rd of the plot = 1/3 \[ \times \] 2,25,000 = 75000

Loss % = \[\dfrac{{Loss}}{{\operatorname{Cos} t{\text{ }}price}}\]\[ \times \]100

\[8\%  = \dfrac{{loss}}{{75000}}\]\[ \times \]100

loss = \[\dfrac{{8 \times 75000}}{{100}}\] = 6000.


Sumit suffered a loss of Rs 6000 on selling 1/3rd of the land 

SP for 1/3rd of the land = 75000 - 6000 = 69,000.

To make a profit of 12% of 2,25,000, is

 

P%= \[\dfrac{p}{{cp}} \times 100\]

\[12 \times \frac{p}{{225000}} \times 100\]

 \[\dfrac{{12 \times 225000}}{{100}}\]=P


Profit = Rs 27,000

Thus, to get a profit of Rs 27,000

SP= 2,25,000 + 27000 = Rs 2,52,000

Sumit has already sold 1/3rd of the land at Rs 69,000 thus he needs to sell the remaining land at Rs(2,52000-69000) i.e, Rs 1,83,000.

Therefore, Sumit needs to sell the remaining plot at Rs 1,83,000.



Conclusion 

Understanding Profit and Loss is an essential skill that helps you make smarter financial decisions in everyday life. Whether you’re shopping, running a business, or solving math problems, these concepts make handling money easier and more enjoyable. Keep practising the formulas and tricks, and soon you'll learn this topic with confidence!

FAQs on Profit and Loss

1. What is Profit and Loss?  

Profit and Loss refer to the financial outcomes of a transaction. Profit is when the selling price is higher than the cost price, while Loss is when the cost price is higher than the selling price.

2. What is the Profit and Loss Formula?  

  • Profit = Selling Price (SP) - Cost Price (CP)  

  • Loss = Cost Price (CP) - Selling Price (SP)  

3. What is Profit and Loss Account?  

A Profit and Loss Account is a financial statement that summarizes the revenues, costs, and expenses of a business during a specific period, helping to determine its net profit or loss.

4. What is the Profit and Loss Format?  

The Profit and Loss format typically includes:  

  • Revenue  

  • Cost of Goods Sold (COGS)  

  • Gross Profit  

  • Operating Expenses  

  • Net Profit or Loss  

5. What is the Profit and Loss Percentage Formula?  

  • Profit Percentage = (Profit ÷ Cost Price) × 100  

  • Loss Percentage = (Loss ÷ Cost Price) × 100  

6. What are some Profit and Loss Formula and Tricks?  

  • Use percentages for quick calculations.  

  • If Profit % + Loss % = 100%, the transaction results in no gain or loss.  

  • Discounts reduce cost price and can affect profit margins.  

7. How to Calculate Profit and Loss?  

  • Profit: Subtract the cost price from the selling price.  

  • Loss: Subtract the selling price from the cost price.  

  • Apply the profit and loss percentage formula for precise calculations.

8. What is a Profit and Loss Calculator?  

A Profit and Loss calculator is an online tool that simplifies calculations by providing instant results for profit, loss, and their respective percentages based on the input values of cost price and selling price.

9. What is the Discount Formula for Profit and Loss?  

Discount = Marked Price - Selling Price  

Discount Percentage = (Discount ÷ Marked Price) × 100  

10. What is the Difference Between Loss and Profit?  

Loss occurs when the cost price is greater than the selling price, while profit happens when the selling price is greater than the cost price. Both are calculated to evaluate financial performance.