Profit and loss

“Profit and Loss” a concept of mathematics that is used in academic as well as in day to day life. Buying and selling are associated with our daily routine activities.

      When you go to shop, the shopkeeper may gain a profit by selling you an item above its cost price. while on the other hand, if you are good at bargaining ( which I am not ) , you force the seller to sell you the item below its cost price. Then the seller faces a loss. 
 
Thus you can see the importance of the concepts of profit and loss.

Let us get familiar with some terms, for complete understanding of the topic.

  1. Cost price: The price at which an article is purchased is called cost price. It is denoted as CP.

  2. Selling Price: The price at which an article is sold is called selling price. Sometimes it is also called as sale price. It is denoted by SP

  3. Profit or gain: If an item is sold above its cost price then a profit is made. In other words, When selling price is greater than cost price then profit is made by the seller.
    The Profit is calculated as,
                    Profit= Selling Price – Cost Price
         And profit percentage is calculated as
                 

    Profit % = (\frac { selling\quad price\quad -\quad cost\quad price }{ cost\quad price } )\times 100

  4. Loss : When an item is sold below its cost price i.e if the cost price is more than the selling price then the seller faces a loss.
                   The Loss = Cost price – Selling price
     and 

       Loss % = (\frac { Cost\quad price\quad -\quad selling\quad price }{ cost\quad price } )\times 100

           
     Note : Profit and loss are always calculated on cost price. 
  5. Marked Price: It is the price which is labelled in the item. This price is set by the seller. This is also called listed price . It is represented as MP.

  6. Discount: The amount of reduced from marked price of an article for selling is called discount. 

    It can be calculated as
                  discount = Marked Price – Selling Price
     and     

     discount %= (\frac { Marked\quad price\quad -\quad Selling\quad price }{ Marked\quad price } )\times 100

 


 

Important formulas and tricks for calculations of profit and loss

  1.  Profit = Selling Price – Cost Price
    and
    profit and loss formula
  2. Loss =Cost price – Selling price
    and
       

  3. For calculating the selling price:

    i) When Cost price and profit % are given



    ii) When Cost Price and loss% are given

    iii) When Marked price and discount percentage are given.



  4. For finding the Cost Price
    i) For given values of Selling Price and Profit%:



    ii)For given values of selling price and loss%:

Other Tricks

  1. When a person sells identical items ,one at a profit of x% and other at a loss of x% then the seller always incurs a loss . 
  2. If a person A sells an article to a person B with a profit of x% , and B sells the article to C with a profit of y%. Then,

     This is a case of successive profit. 
  3. If a person A sells an article to person B with a Profit of x % and B sells it to C with a loss of  y%. Then,


     Negative answer means a loss is incurred. On the other hand, positive answer means profit is made. 
  4. When A sells an item to B with a loss of x % and B sells to C with a profit of y %.


  5. When a person A sells an article to a person B with a loss of x% , and B sells the article to C with a loss of y%. Then,

    This is a case of successive loss.

Relationship between MP and CP

i) In case of profit – 



ii)In case of loss:

False weight Condition:

When a seller sells his goods at CP but uses false weight. THen 


 

Since we have learned the tricks let us move forward to solve some questions.

Question 1 : A man buys an article for Rs 20 and sells it for Rs 15. Find the loss and loss%.
Solution: Here,
                 Cost Price(CP)= Rs 20
                 Selling Price(SP)= Rs 15
         we know,
                       loss  = CP – SP
                                = 20-15
                                = Rs 5
Therefore,       loss =Rs 5
 and  Loss % = (\frac { Cost\quad price\quad -\quad selling\quad price }{ cost\quad price } )\times 100

 Loss % = (\frac { 20\quad -\quad 15 }{ 20 } )\times 100

              = 25%
Hence, Loss% is 25%

Question 2: Aman purchased a book for Rs 500 and sold it for RS 525.Find the profit%.
Solution: Here,
                 Cost Price(CP)= Rs 500
                 Selling Price(SP)= Rs 525
         we know,
                       Profit = SP – CP
                               = 525-500
                               =Rs 25
Therefore,       profit =Rs 25
 and  Profit % = (\frac { selling\quad price\quad -\quad cost\quad price }{ cost\quad price } )\times 100

       Profit % = (\frac { 525\quad -\quad 500 }{ 500 } )\times 100

                    =5%
Hence, Profit% is 5%

Question 3: If the cost price of an article is Rs 300 and the seller gain a profit% of 20% .Find its Selling Price.
Solution: Given,
                 Cost Price = Rs 300
                 Profit% = 20% 
                 Selling Price = ?
we know,
     
 selling price= (\frac { 100+20 }{ 100 } )×300

                       =  (\frac { 120 }{ 100 } )×300

                      SP = Rs 360
Therefore Selling Price is Rs 360.

Question 4. The cost price of toy is Rs 120 and the seller incurs a loss of 10%. Find the selling price.
Solution: Given,
                 Cost Price = Rs 120
                 Loss% = 10% 
                 Selling Price = ?
We know,

 Selling Price= (\frac { 100-10 }{ 100 } )×120

                       =  (\frac { 90 }{ 100 } )×120

                      SP = Rs 108
Therefore Selling Price is Rs 108.

             

Question 5: The sellling price of an article is Rs 1331. What will be the Cost price if the Profit % is 21%?
Solution: Given,
                         Selling Price = Rs 1331
                        profit% =21%
we know,

Cost Price  = (\frac { 100 }{ 100+21 } )×1331

                       =  (\frac { 100 }{ 121 } )×1331

                      CP = Rs 1100
Therefore Cost Price is Rs 1100.

Question 6: Naveen faces a loss of 4% when he sells an article for Rs 480.Find its cost price.
Solution: Given, Selling price = Rs 480
                             loss% = 4%
  We know,
         

Cost Price= (\frac { 100 }{ 100-4 } )×480

                       =  (\frac { 100 }{ 96 } )×480

                      CP = Rs 500
Therefore Cost Price is Rs 500.

Question 7: A shopkeeper sells his goods at a discount of 4% . If the Selling price is Rs 120, find the Marked price.
Solution: Given, Selling Price= Rs 120
                           and discount% =4% 
let the marked price be Rs x.
We know,
discount %= (\frac { Marked\quad price\quad -\quad Selling\quad price }{ Marked\quad price } )\times 100

⇒ 
4= (\frac {  x\quad -\quad 120 }{ x } )\times 100

⇒   4x= 100x -12000
⇒  96x=12000
⇒  x=125

The marked price is Rs 125.

Question 8: A shopkeeper sold an item at a gain of 10%. After sometime he spent his sale proceedings to purchase the same item again.But this time he sold it at a loss of 10%. Find overall Loss% or profit%.
Solution: Always loss is incurred in this case . 
and the loss% is


Overall loss% =\frac {  10^2 }{ 100 }

                          = 1%  
Therefore overall loss% is 1%.

Question 9 : A shopkeeper gains 10% while buying the goods and gains 20% while selling them. Find the total profit%.
Solution: This is a case of successive profit.
formula used


         Here x= 10
            and y =20
   Overall profit= (10+20+\frac {  10×20 }{ 100 })

                            =
30+1.2

                           = 31.2%
The overall profit%= 31.2%

Question 10: A shopkeeper buys an article with a gain of 15% and sells them with a loss of 10%. Find the overall profit or loss %.
Solution: Here this formula will be used.


here x= 15
and y= 10
                  overall profit/loss% =( 15-10-\frac {  15×10 }{ 100 })%

                  =
5-1.5

                 =3.5%
As The answer is positive means a profit is made.

therefore overall profit is 3.5%.



 

It is to be noted that the concept of profit and loss and percentage are interlinked. Thus the concept of percentage plays a huge role. 
I have tried to explain the percentage as easy as possible. Click the link below to learn percentage.
Basic concepts of percentage


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