PROFIT AND LOSS

PROFIT AND LOSS 

SOME BASIC FORMULA E

1) Gain on Rs. 100 is Gain per cent

2) Loss on Rs. 100 is Loss per cent

 

Example:  The cost price of a shirt is Rs. 200 and  selling price is Rs. 250. Calculate the  % profit.

Solution :  We have, C.P.= Rs. 200, 

                                S.P = Rs. 250.    

                   Profit = S.P. - C.P.

                                250 - 200 = Rs. 50.

                   

               

               

Example: Anu bought a necklace for Rs. 750 and sold it for Rs. 675. Find her percentage loss.

Solution : Here. C.P. = Rs. 750.

                         S.P. = Rs. 675.

                          Loss = C.P. - S.P. = 750 - 675 = Rs. 75.

                     

                    

3) When the selling price and gain% are given:

4) When the selling price and loss% are given:

5) When the cost and gain per cent are given:

6) When the cost and loss %  are given:

Example: Mr. Sharma buys a cooler for Rs. 4500. for how much should he sell so that there is a gain of 8%?

Solution: We have, C.P. = Rs. 4500,  gain% = 8%.

 

          

              =   4860

Example: By selling a fridge for Rs. 7200, Pankaj loses 10%. find the cost price of the fridge.

Solution: We have. S.P. = Rs. 7200, loss% = 10%.

                       

                        

                                   

                                       

                                       

SOME USEFUL SHORT-CUT METHODS

1) If a  man buys x items for Rs. y and sells z  items for Rs. w, then    the gain or loss per cent made by him is

     

Example:  If 11 oranges are bought for Rs. 10 and sold at 10 for Rs. 11. what is the gain or loss%?

Solution:  

                  

                                   

                                    

2) If the cost price of m articles is equal to the selling price of n articles, then

Example : If the selling price of 12 articles is equal to the cost price of 18 articles, what is the profit % ?

Solution : 

                       

                                           

                     

                                            

3) If an article is sold at a price S.P.1, then % gain or % loss is x and if it is sold at a price S.P.2, then % gain or % loss is y. If the cost price of the article is C.P., then

           

( Negative for % loss)

Example : By selling an article for Rs. 450, a man loses 25%. At what  price will he sell in order to gain 50%?

Solution: Here,  S.P1= 450, x = 25, y = 50

                         

                       

                               

                             

4) If 'A' sells an article to 'B' at a gain/loss of m% and 'B' sells it to 'C at a gain/loss of n%. If 'C' pays Rs. z for it to 'B' then the cost price for 'A' is

where m or n  is -ve, of it indicates a loss, otherwise it is +ve.

Example: Ravi sells a radio to Sohan at a gain of 17% and Sohan sells it to Rajesh at a loss of 25%. If Rajesh pays Rs. 1053 to Sohan, what is the cost price to Ravi?

Solution: We have, m = 17. n = -25, z = Rs. 1053.

               Cost Price of radio to Ravi is

         

   

   

         

5) When two different articles are sold at the same selling price getting gain/loss of x% on the first and gain/loss of y% on the second, then the overall %gain or %loss in the transaction is given by

Example : A man sold two almirahs for Rs. 4800 each. One one, he gains 30% and on the other, he loses 20%. How much he gain or lose in the whole transaction ?

Solution : In the first almirah % gain = 30% = x

               in  second almirah % loss = -20% = y

                

            

            

            

6) When two different articles are sold at the same selling price and % gain on first article = % loss on second article so, always there is overall loss in the transaction

               

Example : Two watches were sold at Rs. 850 each. On one a gain of 15% is made and on the other, a loss of 15%. How much % loss or % gain is made in the whole transaction?

Solution: Here the S.P. of  two watches are same.

% gain on one watch = % loss on other watch = 15

therefore 

                 

                              

7) A merchant uses faulty measure and sells his goods at gain/loss of x%. The overall % gain/loss(G) is given by

Example: A dishonest shopkeeper professes to sell goods at his cost price but uses a false weight of 950 gms, for each kilogram.  Find his gain percentage?

Solution: 

                 

                 

                  

                              

8) A merchant uses y% less weight/length and sells his goods at gain/less of x%. The overall % gain/loss is given by

Example : A shopkeeper sells the goods at 44% loss on cost price but uses 30% less weight. What is his percentage profit or loss?

Solution : Here, x = -44 and y = 30

                             

                                                                    

                                                                    

9) If two successive discounts of x% and y% are allowed on the marked price of the item, then after discount customer has to pay, 

10) If three successive discounts of x%, y% and z% are allowed on the marked price of the item, then after discount customer has to pay,

Example: A shopkeeper offers 15% discount on all plastic toys. He offers a further discount of 4% on the reduced price to those customers who pay cash. What does a customer have to pay in cash for a toy of Rs. 200?

Solution: