Problems on Ages

Simple problems:



1.The present age of a father is 3 years more than three times 
  the age of his son.Three years hence,father’s age will be 10 
  years more than twice the age of the son.Find the present age
  of the father.

  Solution: Let the present age be 'x' years.
            Then father's present age  is 3x+3 years.
            Three years hence
            (3x+3)+3=2(x+3)+10
                  x=10
            Hence father's present age = 3x+3 = 33 years.


2. One year ago the ratio of Ramu & Somu age was 6:7respectively.
   Four years hence their ratio would become 7:8. How old is Somu.

   Solution: Let us assume Ramu &Somu ages are x &y respectively.
             One year ago their ratio was 6:7
             i.e  x-1 / y-1 = 7x-6y=1
             Four years hence their ratios,would become 7:8
             i.e   x-4  / y-4 = 7 / 8
                       8x-7y=-4
              From the above two equations we get y= 36 years.
                  i.e Somu present age is 36 years.


3. The total age of A &B is 12 years more than the total age of 
   B&C. C is how many year younger than A.

   Solution:   From the given data
                  A+B = 12+(B+C)
                  A+B-(B+C) = 12
                  A-C=12 years.
               C is 12 years younger than A 


4. The ratio of the present age of P & Q is 6:7. If  Q is 4 years 
   old than P. what will be the ratio of the ages of P & Q after 
   4 years.

   Solution:     The present age of P & Q is 6:7 i.e
                 P / Q  = 6 / 7
                 Q is 4 years old than P i.e Q = P+4.
                    P/ P+4 = 6/7
                    7P-6P = 24,  
                     P = 24 , Q = P+4 =24+4 = 28
                 After 4 years the ratio of P &Q is 
                     P+4:Q+4
                  24+4  :  28+4 = 28:32 = 7:8        


5. The ratio of the age of a man & his wife is 4:3.After 4 years this 
   ratio will be 9:7. If the time of marriage  the ratio was 5:3, 
   then how many years ago were they married.

   Solution:     The age of a man  is 4x .
                 The age of his wife is 3x.
                 After 4 years their ratio's will be 9:7 i.e
                       4x+4 / 3x+4  =  9 / 7
                       28x-27x=36-28
                            x = 8.
                  Age of a  man is  4x = 4*8 = 32 years.
                  Age of his wife is 3x = 3*8 = 24 years.
                  Let us assume  'y' years ago they were married ,
                  the ratio was 5:3 ,i.e
                       32-y /  24-y = 5/ 3
                          y=12 years
                  i.e 12 years ago they were  married

                                                               

6. Sneh's age is  1/6th of her father's age.Sneh's father's age will 
   be twice the age of Vimal's age after 10 years. If Vimal’s eight
   birthday was celebrated two years before,then what is Sneh's 
   present age.

    a)  6 2/3 years  b) 24 years   c) 30 years   d) None of the above 

         
   Solution:  Assume Sneh’s age  is 'x' years.
              Assume her fathers age is 'y' years.
              Sneh’s age is 1/6 of her fathers age i.e x = y /6.
              Father’s age will be twice of Vimal's age  after 10
              years.
              i.e  y+10 = 2( V+10)( where 'V' is the Vimal's age)
              Vimal's eight  birthday  was celebrated two years before,
              Then  the Vimal's present age is 10 years.
                       Y+10 = 2(10+10)
                          Y=30 years.
              Sneh's present age x = y/6
                    x = 30/6 = 5 years.
              Sneh's present age is  5 years.


7.The sum of the ages of  the 5 children's born at the intervals of 
   3 years each is 50 years what is the age of the youngest child.

   a) 4 years  b) 8 years  c) 10 years  d)None of the above

        
   Solution:   Let the age of the children's be   
               x ,x+3, x+6, x+9, x+12.
               x+(x+3)+(x+6)+(x+9)+(x+12)  = 50 
                       5x+30  =  50
                       5x = 20
                       x=4.
               Age of the youngest child is x = 4 years.


8. If 6 years  are subtracted from the present age of Gagan and 
   the remainder is divided by 18,then the present age of his 
   grandson Anup is obtained. If Anup is 2 years younger to Madan
   whose age is 5 years,then  what is Gagan's present age.

     a) 48 years  b)60 years    c)84 years  d)65 years

     
    Solution:  Let us assume Gagan present age is 'x' years.
                   Anup age  =  5-2 = 3 years.
                       (x-6) / 18 = 3
                        x-6  =  54 
                        x=60 years


9.My brother is 3 years elder to me. My father was 28 years of
  age when my sister was born while my father was 26 years of age
  when i was born. If my sister was 4 years of age when my brother
  was born,then what was the age my father and mother respectively
  when my brother was born.

  a) 32 yrs, 23yrs  b)32 yrs, 29yrs c)35 yrs,29yrs d)35yrs,33 yrs


   Solution: My brother was born 3 years before I was born & 4 
             years after my sister was born.
             Father's age when brother was born  = 28+4 = 32 years.
             Mother's age when brother was born = 26-3 = 23 years.