PROBLEMS ON NUMBERS PARTNERSHIPS ARTHMETIC MATERIAL

                                             PROBLEMS ON NUMBERS PARTNERSHIPS ARTHMETIC MATERIAL

                                                                            PROBLEMS ON NUMBERS



EG:


  (1/3) OF (2/5) OF A NUMBER IS 24 THEN FIND THAT NUMBER?



   (1/3)* (2/5) *X = 24



       X = (24 *3*5)/2


   

          = 180


EG:


  

  IF x2 = 25 FIND X?



    x2-25 = 0


   (X+5)(X-5)



    X=-5 OR X= +5


EG :



  IF (1/6)TH OF (3/7) OF A NUMBER IS 21 WHAT IS 30% OF THAT NUMBER?



    (1/6)*(3/7)*X = 21



      X = (21*6*7)/3


         = 88.2


EG:



 WHEN 14 IS ADDED TO A NUMBER IT BECOMES (5/4) TH OF ORIGINAL NUMBER WHAT



IS 25% OF THAT NUMBER?



         X+14 =  (5/4) X




        4X+56 = 5X


        X = 56



      25% of (56)


        14


EG:


A NUMBER CAN DIVIDED BY 4 THEN IT REDUCED BY 21 FIND THE NUMBER?



               

                    X REDUCED BY MEAN X-21



                     (X-(X/4)) = 21



                     3X/4 = 21


                       X = 28



EG:


A NUMBER WHEN DIVIDED BY 4 IT REDUCED TO 21 FIND THAT NUMBER?




                    X/4 = 21


                   

                     X = 84




EG:


A NUMBER EXCEEDS 20% OF ITSELF BY 40 FIND THAT NUMBER?



                 X-(20%)X = 40



                  X-(X/5) = 40


                  

                    4X =   200


                      X= 50



EG:


A NUMBER IS 68% OF OTHER NUMBER IF THE SUM OF THOSE TWO NUMBERS IS 84% OF 500 FIND THE


LARGER NUMBER?




                   100%X + 68%X= 84%OF 500



                    X =250


EG:


THE SUM OF 3 CONSICUTIVE EVEN NUMBERS IS 108 WHAT WILL BE THE MIBBLE NUMBER?






                             X+X+2+X+4 = 108


                             3X+6 = 108



                                 3x = 108


                                 34 


                      MIDDLE NUMBER = 34+2 = 36




EG:


THE SUM OF 3 CONSICUTIVE NUMBERS IS 27 WHAT IS SQUARE OF MIDDLE NUMBER?




                           X+X+1+X+2 =  27


                         MIDDLE NUMBER = X SQUARE


EG:




RAMU WAS ASKED TO DIVIDE A NUMBER BY 5 BUT WRONGLY MULTIPLIED THE NUMBER WITH 5 HIS ANSWER IS 144


MORE THAN THE CORRECT ANSWER WHAT WAS CORRECT NUMBER?





                                     X


                           (X/5)          5X  




                                 (5X-(X/5)) = 144


                       

                               X = 30


                    X/5 =30/5 = 6


EG:



A NUMBER WHEN MULTIPLIED BY 17 IT INCREASED BY 96 FIND THAT NUMBER?



                         X(17) = X+96





                         16X = 96


                      

                          X =6


EX:


WHEN 84 IS ADDED TO A NUMBER THE NEW NUMBER BECOMES 400% OF ORIGINAL NUMBER?



 

                        X+84   =  X(400/100)



                            3X = 84



                                X = 28


EG:


A NUMBER IS AS MUCH GREATERTHAN 65 AS IS LESSTHAN 105 FIND THAT NUMBER?



                      65<  X < 105



                        85



                    X-65  = 105=X



                       2X = 170


                       X =85


EG:


3 NUMBERS ARE IN THE RATIO 4 : 5 :6 AND THE AVERAGE IS 25 FIND THE  NUMBER?




                          (4X+5X+6X)/3 = 25



                           15X = 25*3


                           X = 5


                        4   5    6



                            (5*5) (6*5)


EG:


2 NUMBERS ARE SUCHTTHAT THE RATIO BETWEEN 4:7 IF EACH NUMBER INCREASED BY 4 THE RATIO BECOMES 3:5 FIND THE LARGER NUMBER?




                         4X+4 =    3

                       .......     ...


                          7X+4       5




                      20X+20  = 21X+12



                    X = 8



                    7X = 7*8 = 56


EG :



THE SUM OF TWO NUMBERS IS 22 FIVE TIMES OF ONE NUMBER IS 6 TIMES OF OTHER NUMBER FIND THAT NUMBER?



                         5X = 6Y



                       X/Y  = 6/5



                           X= 6Y/5



                        (6Y/5) + Y = 22


                              Y = 10


                              X =12


THE SUM OF THREE NUMBERS IS 264 IF THE FIRST NUMBER IS TWICE THE SECOND AND THIRD NUMBER IS 1/3RD OF FIRST 



FIND THE NUMBER?




                  2X+X+(2X)(1/3) = 264



                  3X+ (2X/3) = 264



                     9X +2X = 264 *3



                    11X = 264 *3


                           X = 72



2ND METHOD:



                     X        :              Y      :   Z



                  6           :          3            : 2



                           11P = 264



                         P = 72



EG:


IF THE NUMANATOR AND DENOMINATOR ARE INCREASED BY 20% AND 30% RESPECTIVILY THE FRACTION BECOMES 9/13 WHAT WAS THE ORIGINAL FRACTION?




                     (100X +20x)  = 9


                   .............    ...


                      (100Y+30X)    13



                          12X/13Y = 9/13



                       X/Y = 9/12


EG:


 IF 20% OF THE NUMANATOR AND 30% OF THE DENOMINATOR IS TAKEN THEN NEW FRACTION BECOMES 7/9 FIND THE ORIGINAL


FRACTION?



                     (20%X)/(30%Y) =  (7/9)



                          (2X/3Y)   =  (7/9)


                        X/Y =(7/9)(3/2)


                            

                              X = 7


                           .....  ....


                             Y     6


EG:



IN A 2 DIGIT NUMBER THE DIGITS IN UNIT PRICE IS TWO TIMES MORE THAN THREE OF DIGIT IN THE TENS PLACE IF THE SUM OF TWO DIGITS IS 6 FIND THE NUMBER?




                              Y = 2+3X


                            X+3X+2 = 6


                               4X =4


                              X = 1



                             Y = 6-1 = 5



                            15


EG:



THE SUM OF THE DIGITS OF A TWO DIGIT NUMBER IS 8 IF THE DIGITS ARE REVERSED THE NUMBER IS DECREASED BY 54 FIND THE NUMBER?




                                       X+Y = 8


                     TWO DIGTI NUMBER =  10X+Y            10Y +X



                 (10X+Y) - (10Y-X)  = 54



                        9X - 9Y = 54


                            X-Y = 6


                           X +Y  = 8


EG:


THE DIFFERENCE BETWEEN TWO DIGIT NUMBER AND THE NUMBER OBTAINED AFTER INTERCHANGING 2 DIGITS IS 27


IF THE SUM OF THE TWO DIGITS IS 15 WHAT IS THE TWO DIGIT NUMBER?



             ORIGINAL = 10X+Y


             REVERSE =  10y+X



        (10X+Y)-(10Y-X) = 27


        (10Y+X)-(10X+Y) = 27


             X-Y = 3


              X+Y = 15


          X = 96 OR 69


EG:


THE DIFFERENCE NBETWEEN THE TWO DIGTI NUMBER AND THE NUMBER OBTAINED BY INTERCHANGING THE TWO


DIGIT IS 18 THE SUM OF THE TWO DIGITS OF A NUMBER IS 12 WHAT IS THE PRODUCT OF THE DIGITS OF TWO DIGIT NUMBER?



                         (X-Y) OR (X+Y) = 18/9 =2


                          

                           X+Y = 12


                           X-Y = 2



                              2X = 14


                            X =7 


                       7-2 =5




                 PRODUCT = 5*7 = 35


EG:



THE SUM OF THE SQUARES OF TWO DIGIT IS 80 AND THE SQUARE OF DIFFERENCE IS 36 FIND THE PRODUCT OF TWO NUMBERS?



                          (X-Y)(X-Y) = 36



                           x^2 +y^2 = 80


                          80-2XY = 36


                              XY = 22


EG:


 THE DIFFERENCE OF TWO NUMBERS IS 5 AND THE DIFFERENCE OF SQUARE IS 135 FIND THE SUM OF THE SUMBERS?



                               X-Y = 5


                             x^2-y^2= 135


                     (X+Y)(X-Y) = 135


                       135/5


                                27


                      X+Y = 27

                  ........  ...

                      X-Y    5


                       X = 32

EG:


THE SUM OF TWO NUMBERS IS 29 AND THE DIFFERENCE OF THE SQUARE IS 145 FIND THE DIFFERENCE BETWEEN THE NUMBERS?



                    X+Y = 29


                  x^2 -y^2 = 145



                     (X+Y)(X-y) = 145


                     (X-Y) = 145/29 = 5


EG:


A NUMBER WHEN INCREASED BY 20% GIVES 720 FIND THE NUMBER?


                   100X + 20X = 720


                        120X = 720


                         X = 6


                      100X = 600


EG:


WHEN 60 IS ADDED TO 60% OF A NUMBER THE RESULT IS THE NUMBER ITSELF FIND THE NUMBER?



                     60+(60%X) = 100%X


                       40%X = 60


                     X =150


EG:


WHEN 75 IS ADDED TO 75% OF A NUMBER THE RESULT IS 125% OF THAT ORIGINAL NUMBER?



                      75 +75%X = 125%X


                        75 =  50%X


                       100%X = 150


EG:


THE PRODUCT OF TWO NUMBERS IS 120



THE SUM OF THEIR SQUARE IS 289


FIND THE SUM OF THE TWO NUMBERS?



                      XY - 120



                     x^2 +y^2 =289


           x^2 +y^2+2XY = 289 +2XY


             x^2 +y^2 = 289+2*120


                 x^2 +y^2 = 529


                   X-Y = 7


                    X+Y =23


               X= 15 Y = 8


EG:


THERE ARE TWO NUMBERS SUCHTHAT THE SUM OF TWICE THE FIRST AND THRICE THE SECOND IS 39 BY THE SUM OF THRICE THE FIRST AND TWICE THE SECOND IS 36 FIND THE



LARGER OF THE TWO NUMBERS?


                   3Y+2X = 39


                    2Y+3X = 36


                     X = 6


                      Y =9


EG:


SHANKAR GETS 3 MARKS IN EXAMINATION FOR EACH CORRECT ANSWER 2 MARKS FOR EACH WRONG ANSWER HE ATTEMPTS ALL THE 30 QUESTIONS AND SCORED 40 MARKS FIND THE NUMBER


OF HIS CORRECT ANSWERS?


              NO OF QUESTIONS EQUATON =  X+Y = 30


                                         3X-2Y = 40


                          2(X+Y) = 30*2



                          X =100/5 =20



                   





              



                







                 

            PARTNERSHIPS


                                    




                                      partnership


                      

                            

                               simple           compound



partnership:


 

if two are more persons invests certain capital in a business then the deal is called partnership


there are two types of partnerships



simple



compound


simple:

.......


if the capitals are invested  for the same period then the partnership is called simple


partnership in this case profits must be divided in the ratio of their investments



                        inv ratio    a : b


                   

                        profit ratio  a : b




                        p1 : p2 =  i1 : i2


compound :


if the capatals are invested for different time period then it is called compoundpartnership


in this case profits must be divided in the ratio of the products


of respective investments and time periods



                           pr= i1t1 = i2t2



profits can also can be devided in the products form of ratio of investments and time perios


                                              

                            I1TI/I2T2



                         (I1/I2)*(T1/T2)


EG:


IN A BUSINESS A INVESTED 10000 AND B INVESTED 15000 RESPECTIVILY FIND THE SHARE 


OF A IN THE ANNUAL PROFIT OF 40000?




                             A  :     B


                            

                              10000 :  15000


                               2    :   3


            A INVESTMENT (2/5)40000 = 16000


EG:


IN A BUSINESS A ,B INVESTED 8000 AND B INVESTED 12000 RESPECTIVILY  FIND THE SHARE 


OF B IN THE ANNUAL PROFIT OF 25000?


                            A :   B


                         8000 : 12000


                          8 :   12


                         2 : 3


                 B INVESTMENT = (3/5)*25000


                                15000


EG:


IN A BUSINESS A ,B,C INVESTED 20000 AND B INVESTED 30000 C INVESTED 40000 

RESPECTIVILY THEN FIND  C SHARE IS HOW MUCH MORE THAN A IN THE ANNUAL PROFIT OF 45000


                          

                           A   :   B :  C


                           20    30     40



                         2       3      4




                     (4-2)/9 = 2/9


                        (2/9)*45000


                         10000


EG:


IN A BUSINESS A  10000 FS FOR 4 MONTHS B INVESTED 12000 RS


 FIND THE SHARE 


OF A IN THE ANNUAL PROFIT OF 30000?


              

                            A  :  B


                            10*4 :  12*5


                           I1TI  :I2T2


                            2 :3



                   A SHARE (2/5)30000


                      12000


EG:


IN A BUSINESS A INVESTED 10000 AND B INVESTED 15000 RESPECTIVILY SFTER 6 MONTHS B LEFT THE BUSINESS

THEY GOT A ANNUAL PROFIT OF 35OOO THEN FIND A SHARE?


                       

                                 A  : B


                                I1T1 :I1T2


                               10*12 : 15*16


                                  4 :3


            A SHARE : (4/7) *35000


                         20000


EG:


A AND B STARTED A BUSINESS WITH CAPTITAL OF 30000 AND 20000 AFTER 10 MONTHS A LEFT THE BUSINESS


AFTER ONE AND HALF YEAR THEY GOT A  ANNUAL PROFIT OF 44000 THEN FIND B SHARE?



                          A  :  B



                         20 *10  :  20 *18



                          5 :6


B SHARE  (44000) (6/11)



              24000



EG:


A AND B STARTED A BUSINESS WITH CAPTITAL OF 20000 AND 30000 AFTER 6 MONTHS B LEFT THE BUSINESS


AT TIME SAME TIME C JOINED WITH CAPITAL WITH A AMOUNT OF 40000 THEY GOT A ANNUAL PROFIT OF 60000


THEN FIND A SHARE?



                        A :   B   :C



                   20*12 :30 *6 : 40*6


                    4 :3 :4


                    A SHARE (4/11)*66000


                       24000


EG:


A AND B STARTED A BUSINESS WITH CAPTITAL OF 8000 AND 12000 AFTER 6 MONTHS B LEFT THE BUSINESS


AFTER 2 MONTHS  C JOINED WITHA CAPITAL OF 18000 RS THEN THEY GOT THE ANNUAL PROFIT OF 60000


FIND B SHARE?



                      A : B  :C



                   8*12 :  12*16 : 18*14



                   4 :3 :3 



                 B SHARE  : (3/10)* 60000


                            18000


EG:


A STARTED A BUSINESS WITH A CAPITAL OF 20000 AFTER 4 MONTHS B JOINED WITH A CAPITAL OF 30000


ATER ONE YEAR THEY GOT ANNUAL PROFIT OF 50000 FIND A SHARE?


                          A : B



                       30*12 :30*8



                          1:1


                     (1/2)*50000

                           25000


EG:


A STARTED A BUSINESS WITH A CAPITAL OF 10000 AFTER ONE YEAR B JOINED WITH A CAPITAL OF 18000


AFTER 6 MONTHS C JOINED WITH 20000 THEY GOT A PROFIT OF 80000 IN 3 YEARS FIND A SHARE ?


                                 A         B         C


                               10*36    :   18*24  :  18*20


                                    

                                 5              6      5



                          5/16(80000) 


                              25000


EG:


IN A BUSINESS A, B INVESTMENTS RATIO 5 : 3 THEIR INVESTMENT TIMES RATIO 9 :10 IN WHICH RATIO THEY


WILL DISTIBUTE THEIR SHARES?


                             A          B


                            5*9  :  3*10


                            45    :  30


                               3 : 2


EG:


IN A BUSINESS A  INVESTMENT IS 3 TIMES TO B'S INVESTMENT 


A INVESTMENT TIME IS DOUBLE TO B'S INVESTMENT TIME THEN THEY GOT A PROFIT OF 21000


FIND A SHARE ?


                           A  B


                         1*3 : 1


                         2*1 :  1


                A : B :   6 : 1


          

                  A PFOFIT : 


                              (6/7)*21000


                               18000


EG:


IN A BUSINESS A INVESTMENT IS DOUBLE TO B INVESTMENT B INVESTMENT IS 3 TIMES TO C INVESTMENT THEN THEY GOT


PROFIT OF 6000 FIND A SHARE?


                           A   :      B :       C


                       2*3*1          3*1     1



                         6             3       1


                     

                A SHARE (6/10)60000


                              36000


EG:


A,B STARED A BUSINESS A INVESTED 20000 RS IF THE PROFITS AT THE END OF THE YEAR IN THE RATIO 4 : 7


THEN FIND B INVESTMENT?


                                    A           B


                                 20000 : X =   4 :7


                                

                                     X =    (20000*7)/4


                                          35000


EG:


A STARTED A BUSINESS WITH A CAPITAL OF 15000 AFTER 3 MONTHS B JOINED  PROFITS AT THE END OF THE YEAR DISTIBUTED EQUALLY


THEN FIND B SHARE?


                           15000 * 12 : 9*12 =  1 : 1


                               9X = (15000*12)


                                X = 20000


EG:


A STARTED A BUSINESS WITH A CAPITAL OF 30000 AFTER SOME TIME B JOINED WITH A CAPITAL OF 20000


 PROFITS AT THE END OF THE YEAR DISTIBUTED IN THE RATIO 2 : 1 


THEN FIND HOW MANY MONTHS LATER B JOINED IN THE BUSINESS?


 

                               30*12 : 20 *X = 2 : 1


                        

                                X = (30*12)/(20*12)


                                       9 MONTHS



   HOW MANY MONTHS LATER B JOINED = 12 -9 = 3 MONTHS


EG:


A STARTED A BUSINESS WITH A CAPITAL OF 20000 AFTER SOMETIME B JOINED WITH 10000


IN A YEAR A'S SHARE IS 3/4 OF TOTAL PROFIT THEN FTER HOW MUCH TIME LATER B JOINED IN THE BUSINESS?



                             A                    B


                      

                            20000*12               10000*X  = 3 :1



                       

                       X = (20000*12)/(10000*3)



                             8


                   =  12-4 


                        8


EG:


A AND B STARTED A BUSINESS WITH 10000 AND 15000


15 % OF THEIR PROFIT GOES TO CHARITY THEN THEY GOT ANNUAL PROFIT OF  40000


THEN FIND A SHARE?


               A  :  B


             10 :        15


               2  : 3


REMAINING AMOUNT AFER GIVING TO CHARITY =  (40000)*(85/100)


                                             34000


                          (34000)(2/5)


                           13600   



EG:


A AND B STARTED A BUSINESS WITH  15000 AND 21000 RESPECTIVILY 20% OF THEIR PFOFIT SHARE GOES TO CHARITY 



AFTER ONE YEAR THEY GOT A PROFIT OF 60000 THEN FIND B SHARE?


                       

                       (60000)*(80/100)


                            

                            48000



                      A  :  B



                     15 : 21


                     5 : 7


            B SHARE : (48000)(7/21)


                         28000


EG:


A , B STARTED HEIR BUSINESS WITH 8000,12000 RESPECTIVILY THEY DONATED 10% OF THEIR PFOFIT TO 


CAHRITY AFTER ONE YEAR A SHARE 5400 THEN FIND TOTAL PROFIT?


                    A : B


                   8 :12


                   2 :3


                  

                A SHARE  2 -------5400



                B SHARE  3 .......8100


       TOTAL SHARES = 5400 +8100 


                        13500


             TOTAL PROFIT :


                            90% ----------- 13500


                            100%..............?


                       

                      (100*13500)/90



                        15000


EG:


A,B STARTED A BUSINESS WITH 20000,30000 RESPECTIVILY B IS A SLEEPING PARTNER



SO A GOT 20% OF THEIR PROFIT AS SALARY


AFTER ONE YEAR THEY GOT A PROFIT OF 40000 THEN A SHARE?



                   A  : B


                 20 : 30


                  2  : 3


A SALARY 8 THOUSAND



                    (40000*(80/100))


                    

                     32000



THEN A SHARE  = (2/5)*(32000)



                12800


     A TOTAL SHARE =  8000+12800


                     20800


EG:


A,B STARTED A BUSINESS WITH 15000 AND 25000 RESPECTIVILY B IS A SLEEPINGPARTNER IN THAT BUSINESS AFTER ONE YEAR


A AND B GOT PROFIT OF 30000 THEN FIND A SHARE?


                    A  :   B


                   15  :  25


                    3 : 5


      B   5 -------30000


     A     3   ...... 18000




              


            A = 30000-18000


               12000


EG:


IN A BUSINESS A AND INVESTED 25000 AND 40000 RESPECTIVILY IN THAT B IS A SLEEPING PARTNER AFTER ONE YEAR A AND B GOT A PROFIT 


OF 48000 THEN FIND A S MONTHLY SALARY?


                        

                                A        B


                                25     40


                 

                                5        8


                            *6

               B ----- 8  ------- 48000


                 

               A....   5.....*6....  30000


 

           A'S SALARY  = 48000 -30000 



                          18000



        A'S MONTHLYSALARY = 18000/12 = 1500


EG:


A, B STARTED A BUSINESS WITH 10000,15000 AFTER 6 MONTHS A INVESTED 5 THOUSAND RUPEEES


IN A YEAR THEY  GOT A PROFIT OF 44000 THEN FIND A SHARE?



                      (10*6)+ (15*6) :  15*12


                               25   :30



                                5 :6



            A SHARE  :   (5/11)*44000


                                20000


EG:


A,B STARTED A BUSINESS WITH 20000 AND 30000 AFTER 6 MONTHS A INVESTED 10000 MORE AND B ALSO INVESTED



5000 MORE IN A YEAR THEY GOT PROFIT OF 69000 THEN FIND A SHARE?




                           A   :    B



               (20*6 + 30*6    :    30*6  + 35*6)



                        10     :   13




                A SHARE  :      (10/23) * 69000



                              30000


EG:


A,B STARTED A BUSINESS WITH 8000 AND 12000 AFTER 6 MONTHS A INVESTED 4000 MORE BUT B WITHDRAN 2000 RS THEY GOT ANNUAL INCOME OF 84000


THEN FIND A SHARE?



                            A        :   B



                  (8*6 +12*6  )  :   (12*6 +10*6)


                     10  :  11




                        (12000-2000)


                             10000



         A SHARE (10/12)*84000


                  40000



EG:


IN BUSINESS A,B INVESTMENT RATIO IS 4 :5 AFTER 6 MONTHS A INVESTED HALF OF THE INITIAL INVESTMENT 



AGAIN BUT B B WITHDRAW (1/5)TH OF HIS INVESTMENT THEN FIND AFTER ONE YEAR THEY HAVE TO DISTRUBUTE THEY AMONT IN



THEIR PROFITS WHICH RATIO?


                       A    :  B            5 - 5*(1/5)

                                             

                                               5-1 


                                              4


                                              HLF OF THE 4 = 2


                                                4+2 =6


                           A : B


              

                         4*6 + 6*6 : 5*6 +4*6



                               10  :9


EG:


IN A BUSINESS A,B INVESTED IN THE RATIO 5 :8 AFTER 6 MONTHS A INVESTED 20% EXTRA BUT B WITHDRAW 25% AFTER ONE YEAR THEY GOT



PROFIT OF 50000 THEN FIND A SHARE?




                                A            B



                       5*6+6*6       :    8*6+6*6 = 11:14         5(20/100) = 1


                                                                   5+1 =6


                                                                 8*(25/100) = 2


                                                                  8-2 = 6


                             A SHARE (11/25)*50000


                                    

                                        22000


EG:


IN A BUSINESS A , B AND C INVESTED 35000 RS A INVESTED 3000 MORE THAN B B INVESTED 4000 



MORE THAN C THEN IN WHICH RATIO THEY WILL DISTRIBUTE THEIR SHARES?



                                   C = X


                                   B =  X+4


                                   A =  X+7



                              X +X+4+X+7 = 35


                                   X = 8


                             A : B : C


                            15 : 12 : 8


EG:


IN A BUSINESS A INVESTED 1/3RD AMOUNT IN 1/3RD TIME



B INVESTED 1/4TH IN  1/4TH TIME 


C INVESTED REMAINING AMOUNT TOTAL TIME THEN THEY GOT PROFIT OF 34000


FIND A SHARE?


                       A  :  B  :   C


                     (1/3)(1/3)  : (1/4)(1/4)  :(5/12*1)




               C INVESTMENT  =  (1/3)+(1/4)


                                 7/12


                               1-(7/12)


                               

                                  5/12




                          A         B            C



                         (1/9)     (1/16)      (5/12)




                             16: 9:60

                             ............

                               144


                                   

                              16 : 9 :60


                 A SHARE  =  (16/85)*34000


                              6400


EG:


A,B,C INVESTED 32000,36000,AND 46 THOUSAND IN A BUSINESS FIND THE SHARE OF B IN THE ANNUAL 


PROFIT OF 11400?




                                 32 : 36 : 46


                  

                                16 :  18 : 23



                                    57



                       (18/57)*11400


                               3600

EG:


A B AND C INVESTED 40000 AND 64000 AND 72000 IN A BUSINESS IF A RECEIVES 24000 RS LESSTHAN 


C AS HE SHARE IN THE ANNUAL PROFIT WHAT IS THE SHARE OF B?



                                A        B           C



                                 40       64          72



                  PROFIT C -A = 24000


                          B  =  ?



                                5  : 8 : 9


                           C-A = 9-5 = 4


                            4 ----------24000


                            8 ..........?



                              (8*24000)/4


                                  48000


IN A BUSINESS P CONTRIBUTES 45000  FOR 5 MONTHS Q 60000 FOR 5 MONTHS R CONTRIBUTES 80000 FOR 6


MONTHS WHAT IS THE SHARE OF Q IN THE TOTAL 134000?


           

                 45000*5 :   60000*5 : 80000*6



                  15            20        32



            13400*(20/67)


                           40000


EG:


SRINIVAS BEGAN A BUSINESS WITH 13000 AFTER 4 MONTHS SRIDHAR JOINED WITH A CERTAIN CAPTAIL AT THE



END OF THE YEAR THPROFITS WERE DIVIDED IN THE RTIO 5 : 2 HOW MUCH DID SRIDHAR INVEST?


                 


                         P1/P2 = (I1/I2)*(T1/T2)             13000 : 3


                        


                         5/2 = (13000/X)/(12/8)                   12 : X


                       

                            

                               X = (13000*12*2)/(5*8)


                                     7800


EG:


A BEGAN A BUSINESS WITH 45000 AND WAS LATER JOINED BY B WITH 54000 AFTER HOW MANY MONTHS B JOINED IF THE PROFITS AT THE END OF THE YEAR



ARE DIVIDED IN THE RATIO 2 : 1?




                    (2/1) =  (45000/54000)/(12/(12-X)




                             12-X = 5


                           X = 7


EG :


A AND B PARTNERS IN A BUSINESS A CONTRIBUTES 1/4 OF THE CAPTIAL FOR 15 MONTHS AND B RECEIVED 2/3OF THE PROFIT FIND FOR HOW LONG B'S 


MONEY WAS INVESTED?


                      

                         P = IT


                       

                          A        B



            INV           1/4       3/4       =   1 :  3


            TIME          15         X        =   15 :  X


           PROFIT        1/3          2/3     =   1   : 2




                  

                           1/2  =  (1/15)(15/X)


                  

                           X = 10



EG :


RAM INVESTED 1/3 RD OF THE THE CAPTIAL FOR 1/4TH TIME



KRISHNA INVESTED 1/5 TH OF THE CAPITAL FOR 1/2 TIME


AND RAHIM INVESTED REMAINING CAPITAL FOR WHOLE TIME WHAT IS THE


SHARE OF RAM IN THE TOTAL ANNUAL PROFIT OF 78000?


 


         INV              1/3       1/5     1/15


         TIME             1/4       1/2     1



                        (  1/12      1/10    1/15)60


                           5         6        28





                     39..............78000



                      5 ..................?



                        10000


EG:


IN A JOINT VENTURE A,B AND C INVESTED 1/4TH OF THE CAPITAL 1/5 TH OF THE CAPITAL AND THE RESPECTIVILY FIND THE SHARE OF B IN THE TOTAL 


PROFIT OF 600000



                      1/4     1/5       11/20


                       5       4         11          1-(9/20) = 11/20


                 


                         20.............600000


                          5 .................?




                           20..............600000



                           4 .............?



                     25 20    C


                              55%


EG:


A,B AND C INVESTED A TOTAL SUM OF 10000000 IN A BUSINESS A INVESTS 3000000 MORE THAN C B INVEST 



10000000 MORE THAN C THEN  FINE THE SHAR EOF C OUT OF TOTAL PROFIT 


OF 20 LACK RUPEES?




                  A                B        C



               30+C             10+C         C



                      3C+4000000 =  1000000


                            C = 60/3


                                20



                          B=  10+20


                               30%



                  30/100(20000)


                     60000


EG:


A,B,C PURCHASED A FIRM FOR 10000000 RS OF WHICH A PAYS 400000 RS A SELL IT SOAS TO GAIN CERTAIN SUM OF 



WHICH B GETS 2,75000 AND C GETS 175000 RS FIND A'S SHARE IN THE PROFIT?



                            10


                         A   B   C



                        4L     6L



                         2   :   3



                         3..........4.5L


                          2.........?



                       (2*4.5L)/3


                      

                          3L


EG:



IN A BUSINESS THE INVESTMENTS OF A AND B ARE IN THE RATIO  3 :2 IF 10% OF THE TOTAL 


PROFIT GOES TO CHARITY AND A RECEIVED FINALLY 8100 RS FIND THE PROFIT?



 

                              A   :   B


                              3       2



                90%A =   8100


                100%A  =  9000



                                  3 .........9000


                                 2 ...........6000


                                          ..........


                                               15000



EG:


A ANB B INVESTS 5,6 LACK IN BUSINESS A RECEIVES 25% OF THE PROFIT AS SALARY AND BALANCE


IS DIVIDED IF THE TOTAL PROFIT ARE 44000 RS FIND THE TOTAL  ?




                TOTAL PROFIT 44000



                   25% OF PROFIT 11000



                    TOTAL PROFIT - A PROFIT


                       44000 - 11000


                       33000


                      5 : 6


                 11P .........33000


                  5 .............?


                     15000




                   15000 +11000= 26000


EG:


X AND Y STARTED A BUSINESS WITH CAPITALS 20K AND 25K AFTER FEW MONTHS Z JOINED THEM WITH CAPITAL OF 30 THOUSAND



IF THE SHARE OF Z IN THE ANNUAL PROFIT OF 50000 RS IS 14000 RS THEN AFTER HOW MANY DAYS FROM THE BEGINING Z JOINED?


                   X         Y          Z



                20       25            30



                 12      12           (12-X)



                ..............................



                 48       10             6(12-X)


                      18                (12-X)




                      2(12-X) =  14000


                               =  5


EG//;


 A, B,C INVESTED 20000,30000,AND 50000 IN A BUSINESS IN A YEAR THEY GOT PFOFIT OF 60000


 FIND EACH ONE SHARE ?



                                A    :   B   :   C



                             20000     30000     50000


                              2          3         5



                        10 PARTS ------------60000


                          1 PART.............?


                              6000




                     12000   18000       30000


EG:



IN A BUSINESS A INVESTED 1/3RD AND B INVESTED 1/4TH C INVESTED REMAINING AMOUNT TOTAL PROFIT 60000



FIND C SHARE?



                     1 - ((1/3)+(1/4))



                         (4+3)/12



                        1-7/12



                        (5/12)*60000


                       25000



       A SHARE  1/3(60000) = 20000


       B SHARE   1/4(60000) = 15000



           A +B = 35000


            C = 60000-35000 = 25000


MODEL 2 :


                P = IT



 IN THE ABOVE RULT ONLY FOR TO FIND RATIOS



 EG:


A STARTED ONE BUSINESS WITH 20000 AFTER 3 MONTHS B JOINED WITH 40000 AFTER 3 MONTHS C JOINED WITH


60000 THEN FIND THEIR ANNUAL PROFIT IN WHICH RATIO?



                          A       B          C



                      20000       40000     60000


                       1        2            3



             TIME       12M      9M          6M


                          4       3        2



             PROFIT     1*4       2*3       3*2



                         4          6        6


                          2         3        3


EG:


IN A BUSINESS A INVESTED 1/3RD AMOUNT 1/3RD TIME 


B INVESTED 1/6TH AMOUNT 1/6TH TIME C INVESTED REMAINING AMOUNT WHOLE TIME FIND 


TOTAL PROFIT IN WHICH RATIO?





           TOTAL INVESTMENT   6 PARTS


                            A       B        C


          INVESTMENT         2       1        3



            TIME             2       1        6


            PROFIT          4        1           18


EG: 


IN A BUSINESS A,B,C INVESTED TIME 1 : 2 : 3 THEY PROFIT RATIO 2 : 3 : 4


A S INVESTMENT IS 60000 RS FIND C INVESTMENT?



             INVESTMENT = (PROFIT/TIME)


              

                     (2 : 3 : 4/1 : 2 : 3)6


                   12 : 9 :8


                     (8/12)*60000


                     40000


EG:


A STARTED A BUSINESS WITH 30000 THEN B JOINED WITH 40000 THEIR PFOFIT SHARE AFTER THE YEAR IS EQUAL 


THEN FIND HOW MANY MONTHS LATER B JOINED?


                      A           B 



                   30000            40000


    INVESTMENT       3            4


    PROFIT             1           1


    TIME              1/3       :  1/4


                      4 :   3


                    12M       9M


 

        B JOINED 3 MONTHS LATER


EG:


MODEL 3 :


A,B STARTED A BUSINESS WITH 20000 RS AND 30000 RS AFTER 4 MONTHS A INVESTED 5000


B REMOVED 5000 FROM HIS INVESTMENT THEN IN WHICH RATIO THEY WILL DISTRIBUTE THEIR 


ANNUAL INCOME?



                      A                  B


                  2000*4               3000*4


                  30000*8               2500*8


                     4 +10  :         6 +10


                      14    :       16


                       7    :        8


EG:


A,B,C STARTED A BUSINESS WITH 20000 RS AND 30000 RS AND 40000 RS


AFTER 3 MONTHS A INVESTED 10000 RS B WITHDRAW 10000 


C NOT IN A BUSINESS AFTER 6 MONTHS THEN FIND THE RATIO OF THE ANNUAL PROFITS?




                 A                  B               C


            20000*3              30000*3           40000*6


                +                   +                +


            30000*9              20000*9             


              

               11                   9                8


EG:


A AND B STRTED A BUSINESS WITH 30000 AND 50000  RS B IS A SLEEPING PARTNER SO A GOT 20% AS SALARY 


FINALLY THEY GOT PROFIT 90000 FIND THEIR SHARES?



                   TOTAL PROFIT   100%


                      A SALARY        20%


               

                      

                      A           B


                    3000          5000


                     3            5


             REMAINING


                         80%


                      3     5


                     30%     50%


            A SHARE   30%+20%


            B SHARE   50%


              A 45000   B 45000




   



             




               










                   










                     

                   






                                 









 




 







                  


                





















                               


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