Bankrsadda quantitative aptitude material on problems on ages


Bankrsadda quantitative aptitude material on problems on ages


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



    





                              




                  




                      


            

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