profit and Loss dishonest dealer type method explanation

Formula: A dishonest dealer to sell his goods at cost price, but he uses false weight. then the percentage of gain or profit is

      profit% = [Error/(true value - error)]×100
 
            Error = True value - false value.



   Ex 1:   A dishonest dealer to sell his goods at cost price, but he uses a weight of 960 grams foe the Kg weight. then the percentage of gain or profit is

           
                              (40/960)×100  or (40×100)/960
                       
                             = 4¹/₆   %

type 2:

       a grocer sells rice at a profit of 10% and uses a weight which is 20% less. find his total percentage gain.

   sol:

method 1: here he has given 20% less weight. it is not the profit percentage. so we have to find profit percentage with false weight. then we cal easily find net profit with successive profit formula.

   finding profit using false weight:

     if 1000 grams is true value, false value would be 800  (20% less on 1000 grams =( 80/100)×1000

               then profit % =( 200/800)×100.  =>  25%

finding net profit with successive profit formula:      

                                   profit % =     x + y + xy/100

So, 10+25+250/100  =10+25+2.5  =     37.5 %


find more problems with successive profit here

method 2 (shortcut): using formula 

   So

[(10+20 ) / (100 - 20 )] * 100   = 37.5%

method 3 (shortcut): usiing another formula

  the above short cut works well when the percentage is given for false weight. if value are given in data. this short cut formula works well than that

       so the formula is 

                          profit% = {[100 + % profit] [true value/ false value]} - 100

                                                         = {[100+10][1000/800]} - 100
                                                    
                                                         = 37.5 %

PROBLEM 3: A dishonest dealer sells goods at 10% loss on cost price but uses 15 grams instead of 20 grams. what is his percentage profit or loss?

we can solve this problem by any method from those three explained above.... but i am selecting  3rd method. because in data, values are given unlike previous problem. so 3rd method is efficient as         i mentioned above.

   

            profit  or loss% = [100-10][20/15]-100   

( note: in data 10 % loss is given so should take '-' intead of '+'. compare it with above problem.)

                                     =  [90*20/15]-100   = 120-100    =  20%

 since the sign is +ve there is a profit of 20%.

i hope you got method to solve this kind of problems 

try to solve the problems given below.

prob :a dishonest dealer sells the goods at 6¹/₄% loss on cost price but uses 12¹/₂% less weight. what is his percentage profit or loss?




prob : a seller uses 840 grams in place of one kg to sell his goods . find his actual % profit or loss

a) when he sells his article on 4% loss on cost price.
b) when he sells his article on 4% gain on cost price.

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