PROBLEMS ON AGES PERCENTAGES ARTHIMETIC MATERIAL

  PROBLEMS ON AGES PERCENTAGES ARTHIMETIC MATERIAL                                                                                         PROBLEMS ON AGES


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



EG:


     Five years ago laxmi's age was seven times the age of her son at that


time and after 5 years her age will be thrice the age of her son. how old is laxmi now?




  5 years ago  7 :1


  5 years after 3:1



       7x+10 = 3

     ........  ...

        x+10    1



         7x+10 = 3x+30


         4x = 20


           x = 5



   7*5 = 35+5 = 40


METHOD 2:



             7 : 1


             (3:  1)3



             7 : 1


             9 :  3


      2PARTS INCREASED  




           AFTER 5 YEARS BEFORE 5 YEARS 5 TOTAL 10



         2P =10


              P = 5



           (5*7)+5 = 40

EG:


SANDHYA GOT MARRIED 4 YEARS AGO TODAY HER AGE IS 1(1/8) TIMES HER  AGE AT THE TIME OF MARRIAGE 



HER SONS AGE IS 1/12 OF HER AGE WHAT IS THE AGE OF SANDHYAS AGE?




              PRESENT AGE = X



              MARRIAGE AGE = X-4



              X =  1(1/8)(X-4)



              8X = 9X - 36



                X = 36



            (1/12) *36 = 3 YEARS


METHOD 2:



                9 :8 


               1P = 4


          4*9  = 36


         (1/12) *36 = 3 YEARS


EG3:


   MOHAN GOT MARRIED 9 YEARS AGO TODAY HIS AGE IS 1(1/3) TIMES HIS AGE AT THE TIME OF MARRIAGE FIND HIS 



PRESENT AGE?



                  4 : 3


              1P = 9


                4*9 = 36



EG:


MADHU GOT MARRIED 6 YEARS AGO TODAY HER AGE IS 125% TIMES HER AGE AT THE TIME OF MARRIAGE


HER SONS AGE IS ONE TENTH OF HER AGE?




HER SONS AGE IS?



                        125%


                   125 :  100



                   5  : 4



            MADHU GOT MARRIED 6 YEARS AGO



               1P  =6 


              

             SO 5*6  =30


             HER SONS AGE IS ONE TENTH OF HER AGE (1/10)*30 = 3 YEARS


EG:


AGES OF 3 PERSONS ARE IN THE RATIO 5 : 7 :9 SUM OF SQUARES OF THE AGES OF PERSONS EXCLUDING THAT


OF YOUNGEST PERSON IS 3250 WHAT WILL BE THE RATIO OF THEIR AGES AFTER 10 YEARS?



                    7 x^2 +9 x^2 = 3250



                        16 x^2 = 3250


                          x^2 = 3250/16


EG:

IN 10 YEARS THE AGE OF ROHIT WILL BE 3 TIME THAT OF HIS AGE 6 YEARS AGO WHAT IS THE PRESENT AGE?


                   NOW X 


                  AFTER X+10


            

                         X+10 = 3(X+6)


                         2X = 28



                        X = 14


EG:


  RAM WILL BE 5 TIMES AS OLS AS HE IS NOW AFTER 8 YEARS HOW MANY YEARS HENCE WILL BE 10 TIMES


 AS OLD AS HE IS NOW?



                          PRESENT AGE = X


             AFTER 8 YEARS =  X+8


                        X+8 = 5X


                        X= 2


              10*2 = 20YEARS


                 

                  20-2  =18 YEARS


EG:


RAKESH IS 30 YEARS YOUNGER THAN HIS AUNT TODAY FIVE YEARS AGO RAKESH WAS (1/4) AS OLD AS HIS AUNT 


HOW OLD WILL RAKESH AUNT BE 8 YEARS HENCE?



                     

                   5 YEARS AGO   1:  4


                          3P =30


                          P =10


      

               10*4 = 40 + 5 =  45+8=    53




EG:


    SAMPATH IS AS MUCH YOUNGER TO VAMSI AS HE IS OLDER TO RAKESH IF THE SUM OF THE AGES OF VAMSI AND RAKESH IS 56 YEARS HOW OLD IS



  SAMPATH NOW?



                          R      S         V



                       SAME DIFFERNCE                         

                                 

                  

                                   IF A,B,C ARE IN AP 




                                   B= (A+C)/2



                             56/2 = 28


EG:


P IS AS MUCH YOUNGER TO Q HE IS OLDER TO R IF THE SUM OF THE AGES OF Q AND R IS 50 YEARS



WHAT IS THE DIFFERENCE BETWEEN AGES OF P AND Q?



                       P,Q,R IN A P



                    (P+Q)/2


                        50/2 


                         25


EG:


SAHITHI'S AGE IS (1/6) TH OF HER FATHERS AGE SAHITHIS FATHER AGW WILL BE TWICE OF KAMALS AGE



AFTER 10 YEARS . IF KAMALS 8 TH BIRTHDAY WAS CELEBRATED TWO YEARS AGO THEN WHAT IS SAHITHIS PRESENT AGE?



                       8 YEARS KAMAL



                           8 +2 = 10 YEARS PRESENT


                      AFTER 10 YEARS 20



                    HIS FATHER DOUBLE



                       40  : 20


                         PRESENT FATHER AGE



                        40-10


                             30




                        (1/6)*30



                          5 YEARS


EG:



  3 YEARS AGO THE FATHERS AGE WAS TWICE THE AGE OF HIS FOUR DAUGHTERS IN 3 YEARS TIME THE AGE OF


HIS FOUR DAUGHTERS.IN 3 YEARS TIME THE FATHERS AGE WILL BE EQUAL TO SUMOF AGES OF THE DAUGHTERS 


FIND THE PRESENT AGE OF FATHER?



                         

                          FATHER       4 DAUGHTERS


                        2X               X



                           1                  1


                     2X+6                X+24



                 2X+6  =   1

                .....     .....


                 X+24       1



                    2X+6 =  X+24


                 2*18 = 36

            PRESENT = 36 +3


                    = 39


EG:


WHEN I ADD 4 TIMES MY AGE 4 YEARS FROM NOW TO 5 TIMES MY AGE 5 YEARS FROM NOW I GET


10 TIMES MY PRESENT AGE HOW OLD I WILL BE 3 YEARS FROM NOW?


                 PRESENT AGE  X


           4(X+4) + 5 (X+5)  = 10X


                  X = 25+16


                     = 41


       AFTER 3 YEARS = 44 YEARS


EG:


 THE RATIO OF AGES OF A MOTHER AND HIS SON IS 2 :1 MOTHER WAS 24 YEARS OLD WHEN SHE GAVE


BIRTH TO HER ONLY DAUGHTER WHO IS 6 YEARS YOUNGER TO HER ONLY SON FIND THE PRESENT AGE OF 



MOTHER AD SON (IN YEARS)


                  36 ,18


EG:



 WHEN I WAS MARRIED 10 YEARS AGO MY WIFE IS THE 6TH MEMBER OF THE FAMILY TOADY MY FATHER DIED AND A BABY BORN TO ME THE AVERAGE AGE OF MY FAMILY


A BABY BORN TO ME THE AVERAGE AGE OF MY FAMILY DURING MY MARRIAGE IS SAME AS TODAY WHAT IS THE AGE OF FATHER WHEN DIED?



                   MARIAGE AGE             =        PRESENT AGE



            F+ X1+X2+X3+X4+X5 =  (X1+X2+x3+X4+X5+50)+0


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


                6                       6



                      F = 50



                     10 YEARS AGO = 50


                      PRESENT  = 60


EG:


 THE AGE OF THE TWO FRIENDS WERE IN THE RATIO OF  6 :5 IF THE SUM OF THEIR AGES IS 55 THEN AFTER



HOW MANY YEARS THEIR AGES WILL BECOME  8 :7


                    11P = 55



                    P =5 



                     2*5 = 10


EG:


THE SUM OF THE AGES OF SUNIL AND HIS FATHER IS 46 YEARS 3 YEARS BACK FATHERS AGE WAS 4 TIMES SUNILS AGE FIND PRESENT AGE OF SUNIL?



                      S+F  =46


       3 YEARS AGO   =40 YEARS


   AT THAT TIME  4 :1


                    5P = 40


                     P = 8



                     8 +3 = 11



EG:



 AFTER 30 YEARS A'S AGE IS 3 TIMES TO THE PRESENT AGE THEN FIND A AGE?



                    PRESENT AGE  X



                       X+30  = 3X



                       2X = 30


                        X = 15


EG:


THE  RATIO OF THE AGES OF MR RAO AND HIS SON I1 6 : 1 AFTER 5 YEARS THE RATIO WILL BE 7 :2


WHAT WILL BE THE AGE OF MR RAO?



                       6 :1


                       7 : 2



                   1 PAR 5 YEARS


           

               5*6 


                 30 YEARS


EG:


THE AGES OF A FATHER AND HIS DAUGHTER ARE IN THE RATIO  4: 1 IF 5 YEARS AGO THEIR AGES WERE IN THE


7 :1 FIND THE AGE OF FATHER AND PARENT?





                           4 :1 


                          7 :1


            MULTIPLE 1ST EQUATION WITH1 ( 4 :1) 2 = 8 : 2


                                                

                                                    7 : 1


                       1 PART = 5



                          5*6 = 30


EG:


5 YEARS AGO LAKSHMI'S AGE WAS 7 TIMES THE AGE OF HER DAUGHTER AT THE TIME AFTER 5 YEARS HER AGE WILL BE



THRICE THE AGE OF HER DAUGHTER HOW OLD NOW?



                      7  :  1



                      (3 :1 )3




                      7 :1


                     9 :3


                    

                 2P =10


                           P = 5


                  7*5 = 35



            NOW 35+5 = 40


EG:


MR KRANTHI IS 4 TIMES AS OLD AS BINDU  3 YEARS HENCE THE SUM OF THEIR AGES WILL BE 41 YEARS


WHAT IS THE AGE OF KRANTHI?


                   


                  4X  : X



                  4 : 1


               + 3 YEARS = 41


                   MINUS     6


                    ...........

                          35


             

                       5PARTS  ----------- 35



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


   ANS  28



EG:


PHANI IS AS MUCH YOUNGER TO MICHAEL AS HE IS OLDER TO RAMESH IF THE SUM OF THEIR AGES OF


MICHAEL AND RAMESH IS 48 YEARS FIND THE AGE OF PHANI?


                  V- P  =  P-R



                 V+ R = 48


          V+R = 2P



                 2P = 48



                        P =24



EG:



THE SUM OF THE AGES OF RAMANA AND RAJESH IS 56 YEARS 6 YEARS AGO THE RATIO OF THE AGES WAS 7 :4 HOW OLD IS MR RAJESH NOW ?





                    RAM+RAJ = 56


                      7 :4 


             -6 *2 = -12


             56


            -12


            ....


              44





                     7 :4 


                 11P = 44


           P =4 



       6 YEARS BACK  = 4 *4 = 16



             +6 =  16 +6 = 22


EG:


IN 8 YEARS THE AGE OF RAHUL WILL BE  4 TIMES THAT OF HIS AGE 13 YEARS AGO WHAT IS THE PRESENT AGE?



                       RAHUL


              X+8          X-13



            (X+8)  =  4(X-13)



                 3X = 60


                 X = 20




EG:



THE PRESENT AGE OF PRANATHI IS TWICE THE AGE OF SARADA 3 YEARS AGO IF PRANATHI IS 2 YEARS OLDER TO SARADA WHAT IS THE PRESENT AGE OF PRANATHI?




                P,S


                3  YEARS AGO = S-3


                P 2(S-3)


               P = S+2



                    P-2 = S


                 P = 2(P-5)


                

                  P = 10


EG:


A MOTHER HAD 3 SONS THEY WERE BORN AT AN INTERVALS OF 3 YEARS THE TOTAL AGE OF 3 SONS IS 24 YEARS WHAT IS THE AGE OF YOUNGEST


SON?



                     X+X+3+X+6  = 24


                  3X+9 = 24


                      3X = 15


                       X =5


EG:


 NEELIMA GOT MARRIED 4 YEARS AGO TODAY  HER AGE IS 1(1/6) TIMES THE AGE AT THE TIME OF HER MARRIAGE HER SONS AGE IS


(1/14) OF HER AGE WHAT IS THE AGE OF NEEELIMA'S AGE?


                           (X-4) (1(1/6)) =X


                              (X-4)(7/6) = X


                             X =  28


                   (1/14)*28 = 2


EG:


THE RATIO OF THE PRESENT AGES OF TWO BROTHERS IS 1 :2 AND 5 YEARS BACK THE RATIO 


WAS 1 :3 WHAT WILL BE THE RATIO OF THEIR AGES AFTER 5 YEARS?


               

                          1 : 3



                         1  : 2



                          (1:2) 2 = 2 :4



                        1 :3


                        2 :4


     AFTER FIVE YEARS +1 TO RATIO = 3 : 5


EG:


THE RATIO BETWEEN THE SCHOOL AGES OF NEELAM AND SHYAM IS 5 :6 RESPECTIVILY  IF THE RATIO BETWEN


ONE THIRD AGE OF NEELAM AND HALF OF SHYAMS AGE IS 5 :9 


THEN WHAT IS THE SCHOOL AGE OF SHYAM?


                      N :S


                      5: 6


                N/3 : S:2


             (1/3)5   : (1/2)6


               (5/3) : 3


EG:


A MAN IS 24 YEARS OLDER THAN HIS SON IN TWO YEARS HIS AGE WILL BE TWICE THE AGE OF HIS SON


FIND THE AGE OF HIS SON?



                       F -S = 24


                      F : S 


                     2  :1


                   1P = 24


                       -2


                      .....


                        22


EG:

THE AGES OF A AND B ARE IN THE RATIO 4 :1 THE PRODUCT OF THEIR AGES IS 64


WHAT WILL BE THE RATIO OF THE AGES AFTER  4 YEARS?


                   A: B = 4 :1


                        4X,X


                 (4X) (4X) = 64


                       X= 4


EG:


RAJESH WAS N YEARS OLD X YEARS AGO HIS AGE M YEARS FROM NOW WOULD BE EXPRESED AS?



                 N+M+X

EG:


THE RATIO BETWEEN THE PRESENT AGES OF A AND B IS 5 :3 RESPECTIVILY 


THE RATIO BETWEEN THE A'S AGE 4 YEARS AGO AND B'S AGE 4 YEARS HENCE IS 1 :2


WHAT IS THE RATIO BETWEEN  A'S AGE 4 YEARS HENCE AND B'S AGE 4 YEARS AGO?



               A : B = 5 :3



              (5X-4)/(3X+4) = 1/1



                  X = 4



               5X = 20


                     20 : 12


                   +4      -4


                   24 : 8


                   3 :1



EG:


A PERSONS PRESENT AGE IS 2/5 TH OF THE AGE OF HIS MOTHER AFTER 8 YEARS HW WILL BE ONE HALF OF THE AGE OF HIS MOTHER 



HOW OLD IS THE MOTHER AT PRESENT?


                              PERSON            MOTHER



                         (2/5 ) X                 X



                                  2   :  5



                               AFTER 8 YEARS


                                 1 :2



                              (1 :2 ) 3



                             3 : 6


                            

                         2 :5


                         3 :6


                  1 PART = 8 YEARS


                   5*8 =40 YEARS


eg:


RAHUL MARRIED 4 YEARS AGO NOW HIS AGE IS 1(1/8) TIMES AT THE TIME OF HIS MARRIAGE NOW HIS PRESENT AGE?



       1(1/8) (X-4) = X



          X = 36


                   OR


                  9 :8 


                   1 PART 4 YEARS 



                      9 PARTS 36 YEARS


EG:


SHARMA MARRIED 6 YEARS AGO NOW HIS AGE 1(1/3) TIMES AT THE TIME OF HIS MARRIAGE THEN TIND HIS PRESENT AGE?



               4/3(X-6) = X



                  X = 24



                      OR



                     4 : 3


                   1 PAR T 6




                     4 *6 = 24


EG:


AHUJA MARRIED 7 YEARS AGO NOW HIS AGE 125 % AT THE TIME OF HIS MARRIAGE THEN FIND HIS AGE?



              (X-7 ) (125/100)  = X


                 5X - 35 = 4X


                       X = 35


EG:


PRESENT RATIO OF THE AGES OF A AND B IS 3 :4 AFTER  6YEARS THEIR AGES RATIO 4 :5


THEN FIND PRESENT AGE RATIO?


                  3 : 4


                  4 : 5

                  

               1 PART INCREASED


                     6 YEARS


                3 PARTS = 3 *6  = 18 YEARS


EG :


PRESENT RATIO OF AGES OF A AND B IS 3 : 5 AFTER 10 YEARS THEIR AGES ARE IN THE RATIO  5 :7 


THEN FIND PRESENT AGE?



                         3 : 5


                          5 :7


                    2 PARTS INCREASED


                          PART = 5



              3 PARTS  = 15


              5 PARTS = 25



EG:


 PRESENT RATIO OF THE AGES OF A AND B IS 5 :7


AFTER 5 YEARS THEIR RATIO WILL  BE CHANGED TO 3 :4 THEN FIND PRESENT RATIO OF THEIR AGES?


             (5X+5/7X+5) = 3/4



            (5X+5)4 = 3(7X+5)



                   X =5



 A   = 5*5


 B = 35



                          OR



                     5 :7


                    3 :4



                               5 :7


                               2(3) : 2(4)


   

                          5 : 7



                          6 :8


                     1 PART = 5


                   7 PARTS = 35

EG:


PRESENT FATHER IS 7 TIMES TO SONS AGE


AFTER 10 YEARS FATHER AGE IS 3 TIMES TO HIS SONS AGE


THEN FIND FATHER AGE?


                    FATHER          SON

                    7                1



             AFTER 10 YEARS3 TIME SO MULTIPLE WITH 3



                    (3 : 1)3


                     9 :3



              7 :  1


              9 :3



               2P = 10


 P = 5


                  7X = 7 *5 = 35


EG:


5 YEARS BACK RATIO OF THE AGES OF A AND B IS  4 : 7


AFTER 7 YEARS  A AND B AGES RATIO IS 2:3


THEN FIND THEIR AGES?


            5 YEARS BACK   4 :7


            7 YEARS LATER   2 :3



  

      5 YEARS BACK + 7 YEARS LATER  = 12



        (4X+12/7X+12) = (2/3)


    X = 6



    A = 4X = 24


    B = 7X = 42



NOW AGES


        24 + 5 = 29


        42 +5  =47



METHOD 2:


       5 YEARS BACK  4 :7


       7 YEARS LATER  6 :9



             2 PARTS  12


             1 PART = 6


EG:


3 YEARS BACK FATHER AGE IS DOUBLE TO TOTAL AGES OF HIS 4 SONS


AFTER 4 YEARS  FATHER AGE IS DOUBLE TO TOTAL AGES OF HIS 4 SONS


                    

               FATHER       4 SONS



                2              1



                2X           X



 

3  YEARS LATER       2X +6    X +24



                 2X+6 = X+24



                   X +18



                2X = 2*18


                    = 36



AFTER 3 YEARS  36 +3 = 39 YEARS




EG:


PRESENT DIFFERENCE BETWEEN A AND B AGES IS 12 YEARS 


AFTER 10 YEARS  AND B AGES RATIO IS 5 :7


THEN FIND PRESENT AGES?



             10 YEARS LATER  5 :7



 ( 7 -5) =2 PARTS 




           2 PARTS = 12



                   = 6* 5


                  30


 7*6   = 42



                 PRESENT


                         30 -10      42-10


                          20           32



EG:


  PRESENT AGES OF A AND B IS 50 YEARS 


 AFTER 5 YEARS THIER AGEIR AGES RATIO IS 2 :3 THEN FIND PRESENT AGES?



                 PRESENT TOTAL = 50 YEARS


                  AFTER 5 YEARS = 60 YEARS


               ]        5P = 60



                       P =12


                       2 :3


                   2*12 : 3 *12


                    24 : 36

'


          PRESENT 24- 5 =19


                B = 36-5 =29


 


     






                                





                    





                       



              





               
















                            












   



       

   PERCENTAGES



To convert percentage into fractions divide the given value with hundred


To convert fraction into percentage multiple the given fraction with 100%



                     50% = 50/100 = 1/2


            

                     1/2 = 1/2(100%) = 50%


 

EX:

 convert the folowing percentages into fraction 



1) 60% = 60/100 = 3/5


2) 12.5 % = 12.5/100 = 5/40 = 1/8


3) 33 (1/3)% = 100/3 = 1/3


4) 16(2/3)% = 50/(3*100) = 1/6


EX:


convert the following fractions into percentage


1)  (3/4)*100 = 75 %


2) (4/5) * 100 = 80%


3)  (2/3) * 100 = 200/3 = 66(2/3)%


4) (1/5) *100 = 20%


5) (1/12)*100 = 25/3 % = 8 (1/3)%


NOTE:


50% = 1/2


25% = 1/4


12(1/2)% = 1/8


6(1/4)%  = 1/16


66 (2/3)% = 2/3


33(1/3)% = 1/3


16(2/3) % = 1/6


8(1/3)%  = 1/12


75% = 3/4


14 (2/7)% = 1/7


11(1/9)% = 1/9 


9 (1/11)% = 1/11


NOTE:



1/1 = 100%


1/2 = 50%


1/3 = 75%


1/4 = 25%


1/5 = 20%


1/6 = 16 (2/3)%


1/7 = 14(2/7)%


1/8 = 12(1/2)%



1/4 = 11(1/4)%


1/10 = 10%


1/11 = 9(1/11)%


1/12  = 8(1/3)%


FORMULAE:


           1       x%y = (x/100)y


                       (xy)/100


           2       x is what percentage of y


                   what = (100%x)/y



                 is/of just remember



EG:


   IN 250 FIND 30 % VALUE?


         10% = 25


         30 % = 75


EG:


   IN 360 FIND 15%


        10% = 36


         5%   = 18


      15% =  54



EG:

         IN 450 FIND 22 % VALUE?


       

           10% = 45


            

          20%  = 90


          2%   = 9


                ......


                  99


IN 240 FIND 19%?


      20%          48


        -1%         2.4

               ........

                45.6


EG:


   30 % OF 120 = 36


EG:


   IN A CLASS BOYS AND GIRLS ARE IN THE RATIO 3:2 then find percentage of boys 



          total 5 parts


      boys (3/5) * 100 = 60%


     girls (2/5) *100 = 40%


 

METHOD 2


     5 - 100


     2      ?



      5---100


      3   ?


EG:


IN A CLASS BOYS AND GIRLS ARE IN THE RATIO 3:2 then find percentage of boys 

 

boys what percentage more that girls?


    (1/2) * 100 = 50%


EG:


IN A CLASS BOYS AND GIRLS ARE IN THE RATIO 3:2 then find percentage of boys 


girls what percentage more than boys ?



      (1/3)* 100 = 33(1/3)%


EG:


IN A CLASS BOYS AND GIRLS ARE IN THE RATIO 3:2 then find percentage of boys 


Boys is what percentage of girls?


        (3/2)100 = 150%


EG:



IN A CLASS BOYS AND GIRLS ARE IN THE RATIO 3:2 then find percentage of boys 


girls  is what percentage of Boys ?


        (2/5)*100 = 200/3 = 66(2/3) %



MODEL :



 EG:


     A Salary is 20 % less than b salary then b salary is what % more than a salary?


      

             4 : 5


              (1/4) 100 = 25%



         short cut formulae


         (X/(100±X))*100%


MORE - PLUS


DECREASE OR LESS -- MINUS


COMPARE ABOVE PROBLEM


         (20/(100-20))*100   


         (20/80)*100 = 25%


EG:


 A rectangle length increased by 10 % by what percentage breadth has to be decrease sothat no change in its area?



     (10/(100+10))*100



      (10/110)*100

   

           9(1/11)%


EG:


price of a article decreased by 30% by what percentage it sales has to be increase so that these is no effect in revenue?



                          (30/70)*100


                            300/7


                           42(6/7)%


EG:


price of a sugar increased by 20% by what percentage it consumption has to be decreased sothat there is no change 



                         (20/120)*100%


                          16(2/3)%



MODEL:



EG:    


     Population of a town is 5000 in the first year it is increased by 10 % and then 2nd year it decreased by 20 % find the 


find the population after 2 years and the overall percentage 


                  population first year 10% increased so 110/100


                  population second year 20% decreased     80/100




                     5000 *(110/100) * (80/100)


                550*8 


              4400


              (600/5000)*100


               12% decreased


METHOD 2:


                        +10%     -20%


                      ONLY ON TWO PERCENTAGE CHANGES ONLY


                        

                         ((X+Y+(XY/100)) %


                 

                         (10-20-200/100)%


                        

                          -12% DECREASED


EG:


       A rectangle length is decreased by 10% and bredth decreased by 10 %



        find the effect on its area?




             (-10-20+(200/100)%


              -28% decrease


EG:


        thrice of a article first increased by 10% and again increased by 20 % then decrease by 25 %?


        100*(110/100)* (75/100)


     

          99%


       1 percentage decreased


MODEL 3: 


 EG: 


      population of a town first increased by 10 %and then decreased by 205 if the final population is 4400 initial population?


         increased by 10% so 100/110

           

         decreased by  20% so 100/80


         4400*(100/110)*(100/80)


             5000

EG:


   

 A man spends 85% of his income per household items and out of the remaining 50% per transport if he finally saves 900 find his income?


         


                       900*(100/15)*(100/50)


               

                         12500


EG:


 In a college 30% are arts graduates out of the remaining 40% are science graduates out of the remaining 50% are computer



graduates find total no of students?


            



                             -30%        -40%       -50%



                            210*(100/70)*(100/60)*(100/50)


EG:


 The ratio between a ,b,c is 3 :4 :5 a increased by 20% and b increased by 25% and c reduced by 10% then find new ratio?


          


                  300 : 400 : 500


                360 :  400 : 500


                    36 : 50 :45


EG:


Total votes polled in a election is 1200 votes difference between the winning and loosing candidate is 20%



then find how much votes that winning candidate got?



                       100%


                    

                   20%     80%


    

              differcnce 60% = 1200


               1% = 20 votes


             80% = 1600 votes


EG:


 IN A ELECTION BETWEEN TWO CANDIDATES ONE CANDIDATE GOT 60% VOTES AND WON BY 500 VOTES THEN FIND TOTAL VOTES?



                       100%


                     40%     60%



                 DIFFERENCE 20% = 500


                   1% = 25 VOTES


                   TORAL = 100*25 = 2500 VOTES


EG:


TO pass in an exam every guy need 40% marks but one candidate got 40 marks and then failed by 40 marks then 



total marks in that exam?



   pass : 40 + 40



           80


   so pass percentage 40% = 80marks


                    

                  1% = 2 marks


           100% = 200 marks


EG:


 to pass in an exam students need 30 % marks but one student got 100 marks 



he got 10 marks more than pass mark then total marks in that exam?



            pass % pass marks



              30%    100marks - 10 marks


             30%          90 marks


              1%                3 marks



           100%   =  300 marks


Eg


 in an exam a got 32% marks and failed by 9 marks 


b got 40% marks and pass by 15 marks then find total marks in that exam?



     a        32%     -9marks



      b        40%      15 marks


    

     difference    15-(-9)


                  24




          8%        24 marks



          1%             ?





                 1 percent 3 marks 



             total marks 300


Percentage:   


           percentage literally means every hundred  



comparing every quantity with respectto t100 is called percentage



25% = 1/4


a  percentage can be expressed in fraction


25% = 1/4


in aratio = 1:4


and also in a decimal form .25


conversions:



percentage can be converte into fraction by dividing with hundred



45% = 45/100 = 9/20



a fraction can be converted into percentage by multiplying with 100



(3/4)*100 = 75%



60% = (60/100) = 3/5



(4/5) = (4/5)*100 = 80


10 interms of percentage


10*100 =1000%


EG :


  38 IS WHAT PERCENT OF 152



      152  ------------ 100


       38                 ?



EG:


 WHAT PERCENTAGE IS 50 OF 40


    IS/OF *100


EG:


 30% OF A NUMBER IS 60


         30............60


         100.........?



EG:


 20% OF A NUMBER IS 16


100% OF A NUMBER IS 80



EG:



 32% OF A NUMBER EXCEEDS 12% OF THE SAME BY 60 WHAT IS THAT NUMBER?



   32% - 12% = 20%



  20% ----------------60


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



     60*5 = 300



EG:



A NUMBER WHEN INCREASED BY 30% GIVES 780


FIND HUNDRED PERCENT OF NUMBER?




         A NUMBER INCREASED BY 30% SO 130%



     130% NUMBER IS 780



     100 %..........?



             (780*100)130


         600


EG:



 A NUMBER WHEN DECREASED BY 12% OF IT IT GIVES 220 FIND NUMBER?




    DEC BY 12% SO 100-12 =88%



          88%----------220



        100% ............?



            (100*220)/88



           250



EG:



 PRECENTAGE INCREASE = (INCREASE/INITIAL)*100


PERCENTAGE DECREASE = (DECREASE/INITIAL)*100



EG:


  THE NUMBER OF STUDENTS IN A SCHOOL IS DECREASED TO 320 FROM 400 WHAT IS THE PERCENT DECREASED



                   (320/400)*100 = 80


SO 100-80 = 20%



EG:


RAVI SPENDS 76% OF HIS SALARY WHAT HE SAVING IF HIS TOTAL SALARY IS 4000



76% ---------- 3040



                       4000


                       3040

                   ...........


                       960



EG:


IN AN ELECTION BETWEEN TWO CANDIDATES A CANDIDATE GOT 38 % OF VOTES POLLED AND LOST TO HIS RIVAL BY 3600 VOTES FIND TOTAL?


                    100


                 62    38



   62-38 = 24%


     24% - 3600


     100%--?



EG:


  IN AN ELECION BETWEEN A AND B A GOT 60% OF VOTES WON BY MAJORITY OF 1800 VOTES FIND THE TOTAL NUMBER OF VOTES POLLED?


                            100


                        

                      60%     40%



                         20% ------------1800


                         100% ........?


                 1800 *5 = 9000


EG:


 IN A SCHOOL OF 300 STUDENTS 70% OF STUDENTS BOYS


 20% OF THE BOYS ARE ABSEST THEN HOW MANY BOYS ARE PRESENT?



BOYS = 70% OF TOTAL ABSENT 20% OF BOYS 


        20% OF 70% OF TOTAL


         14% OF TOTAL


      (14/100)*300


        42


EG: 


 IN A SCHOOL OF 300 STUDENTS BOYS ARE 70% 


IF 30% OF GIRLS ARE ABSENT FIND THE TOTAL NUMBER OF GIRLS PRESENT?


   70% = 210


 300 - 210 =90


 30% OF GIRLS ABSENT 


SO 30% OF 80 = 27


  90-27 = 63


EG:


IN A SCHOOL OF 400 STUDENTS 40% ARE GIRLS 30% OF THE BOYS AND 50%OF THE


GIRLS FAILED IN AN EXAM EHAT PERCENTAGE OF THE STUDENTS IN A SCHOOL PASSED THE EXAM?


                          TOTAL 100 PERCENT


                                   100


                            60             40 

  


                          18  42          20  20


  42 +20 = 62%



EG: 


A STUDENT HAS TO GET 38% OF MARKS TO PASS THE EXAMINATION ARUN GOT 81 MARKS BUT FAILED BY 14 MARKS FIND THE MAXIMUM MARKS IN AN EXAM?




                 38% = 81+14 = 95



                  38% ------95


                 100%........?


                 (100*95)/38


                      250


EG:


 A STUDENT HAS TO GET 44% OF MARKS TO PASS THE EXAMINTION RAMYA GOT 143 MARKS WHICH ARE  


33 MARKS MORE THAN NECESSARY TO PASS THE EXAM?



                  44----------110


                  100------?




                   (100*110)/44


                      250


EG:


60 LITERS OF A MIXURE WHICH CONTAINS MILK AND WATER HAVE 35% OF WATER IF 10 LITERS OF MILK IS ADDED


WHAT WILL BE THE PERCENTAGE OF WATER IN THE RESULTANT MIXURE?



                           60



                        35%      65%


                       39         21


            plus 10 LITER MILK 10


                        39+10


                         49            21



(21/70)* 100 =30% 









                  


                                                                                                           










                               





                          









 


     








       


               

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