Profit and Loss: Concept, Formulas,Solved examples and Worksheets

you go to market to purchase your stationary or any other items, Sometimes what happens is the vendor sells you the item at a price higher than its maximum retail price , and you end up paying an extra amount for it .if you are facing a loss so the vendor must be getting profit.These are the simple terms what we commonly use while purchasing and selling something. By means of this article you will be building a strong foundation in  Profit & Loss as well as  you will be solving complex problems in a matter of minutes. Let's get started

What is Profit and Loss 

Before we talk of Profit and Loss let me introduce you  with some new terms that we will be working with most of the times in this chapter.

Cost Price : 

It is the amount that we pay to puchase an item or items.If you pay $5 for a pen so it will be its cost price.We say it C.P in short.

Selling price : 

It is the amount we will be getting when we sell our purchased item.we call it S.P in short

Now you are familiar with C.P and S.P, let's define Profit & Loss

Profit :

When cost price of an article is less than its selling price then it is called a profit.

Profit = S.P -C.P 

Example 1: Suppose angela buys 15 kg rice for $12 and sells it for $15. we can say that angela made a profit of $3. 

Profit = S.P -C.P 

           = $15 - $12 

           = $3

Whenever C.P is subtracted from S.P we get a  + ve number in the case of Profit.

Example 2 : Dyna brings a packet of 15 pens for $2 each and sell the packet at $45 .

Profit = S.P of 15 pens - C.P of 15 pens

           = $45 - $15×2

          = $15

Loss :

When the cost price of an article is more than that of its cost price then it is called a Loss.

Loss = S.P -C.P

Example 1 : John pays $500 for a painting and sells it for $400 to Mike.

We can say that John faces a loss of $100 .

Loss = S.P -C.P

         = $400-$500

         = -$100

Note : Minus sign indicates a loss.To avoid minus sign we can also write 

Loss = C.P - S.P

Example 2 : A man pays £100 for his spectacles while it costs the vendor for £150.

Profit = S.P -C.P 

           = £100 - £150

           = -£50

The vendor incurred a loss of  £50

Percentage Profit & Percentage Loss

We know how profit & loss is calculated now let's look at the formulas to calculate percentage profit and percentage loss.

Percentage Profit = \( {S.P -  C.P \over C.P } \times  100 \) 

                              = \( {Profit \over C.P } \times  100 \) 

Percentage Loss = \( {S.P -  C.P \over C.P } \times  100 \) 

                            = \( {Loss \over C.P } \times  100 \) 

Example 1: A laptop was purchased for $800 and sold for $920. Find the profit percentage.

Cost Price of Laptop  (C.P) = $800
Selling Price Laptop  (S.P) = $920

Profit  = S.P - C.P 
           = $920 - $800
           = $120

Percentage Profit = \( {Profit  \over C.P } \times  100 \) 

                            = \( {$120  \over $800 } \times  100 \) 

                            = 15% Profit

Example 2 : A television purchased for $900 is sold for $810. Find the percentage loss.

Cost Price of television (C.P) = $900

Selling Price of television (S.P) = $810

Loss  = C.P - S.P 

           = $900 - $810

           = $90

Percentage Loss = \( {Loss \over C.P } \times  100 \)
 

                            = \( {$90  \over $900 } \times  100 \)
 

                            = 10% Loss

How to Calculate C.P when S.P and Percentage Profit/Loss known

In case of profit, The Cost Price (C.P ) is computed by this expression : 

\( CP = SP \times \frac{100}{100 + \text{Profit}\%} \)


Example 1: A bicycle is sold for $690 at a 15% profit. What is the cost price?

Selling price of bicycle = $690
Pofit Percent = 15 %

Now apply the formula to calculate Cost price of bicycle.

\( CP\) = \( $690 \times \frac{100}{100 + \text{Profit}\%} \)

\( CP \)  = \(\frac{69000}{115} = \$600\)

In case of loss .The Cost Price (C.P) 

\( CP = SP \times \frac{100}{100 - \text{Loss}\%} \)

Exmaple 1 : A camera is sold for $1,260 after a 10% loss. Find the cost price.

Selling price of bicycle = $ 1,260
Loss Percent = 10 %

Now apply the formula to calculate the C.P

\( CP \) = \( $ 1,260 \times \frac{100}{100 - \text{10}\%} \)

\( CP  =  \frac{126000}{90} = $1400\)

How to Calculate S.P when C.P and Percentage Profit/Loss known

When profit percent is given then the expression to calculate S.P .

\( SP = CP \times \frac{100 + \text{Profit}\%}{100} \)

Example 1 : A pair of shoes is bought for $120 and sold at a 35% profit. Find the selling price.

Cost Price of shoes =  $120
Profit Percent  =  35%

Apply the formula 

\( SP = \$120 \times \frac{100 + 35}{100} \)

\( SP \) = \( 120 \times \frac{135}{100} \)

When Loss percent is given then the expression to calculate S.P .

\( SP = CP \times \frac{100 - \text{Loss}\%}{100} \)


Example 1 : A printer costs $600 and is sold at a 10% loss. Find the selling price.

Cost price of printer = $600 
Loss percent = 10%

\( SP \)  = \( $600 \times \frac{100 - \text{10}\%}{100} \)

\( SP \) = \( $6 \times $90 \)

\( SP = $540 \) 

Marked Price : A price at which a seller gets profit even after giving discount on it.

Suppose, Marked Price of an article is $150 and its cost price is $100 .The seller sold it at 40% discount then what would be the selling price of the article and the profit earned by the Seller 

Marked Price= $50

Discount.       = $50×40% 

                        = $50×40/100

                        = $20

Selling price of the article = Marked Price - Discount

= $150- $20 
                                              
=$130

Profit Earned by the Seller /Markup

= $130 -$100

= $30

Profit percent of the seller 

= \(\text{Profit %} = \frac{\text{Profit}}{\text{Cost Price}} \times 100 \)

= \(\frac{\$30}{\$100} \times 100 \)

= 30%

Profit and loss Formulae 

• \(Profit = S.P  - C.P \)

• \( Loss = C.P - S.P \) 
  
  
• \( CP = SP \times \frac{100}{100 + \text{Profit}\%} \)
  
  
• \( CP = SP \times \frac{100}{100 - \text{Loss}\%} \)
  
  
• \( SP = CP \times \frac{100 + \text{Profit}\%}{100} \)
  
  
• \( SP = CP \times \frac{100 - \text{Loss}\%}{100} \)
  
  

• \( \text{Profit %} = \frac{\text{Profit}}{\text{C.P.}} \times 100 \)
  
  

• \( \text{Loss %} = \frac{\text{Loss}}{\text{C.P.}} \times 100 \)
  
  

• \( \text{Markup %} = \frac{\text{Markup}}{\text{Cost Price}} \times 100 \)

Profit and Loss FAQs

Q 1 : What is the condition for profit ?

Ans : There is a profit when S.P > C.P.

Q 2 : What is the condition for Loss ?

Ans : There is a loss when C.P > S.P.

Q 3 : Why Profit and Loss is always calculated on Cost price?

Ans : C.P is the investment that is initially made.

Q 4 : Is successive discount equal to the sum of discounts ?

Ans : No ,successive discount is not equal to the sum of discounts.

Net % discount is calculated by:

= a +b + ab/100

Profit and loss worksheets

Here are given some Solved and unsolved worksheets that will help you consolidate you concepts.

1. Year 7 Profit and loss worksheet