Question

The sum of the present age of a father and a son is 54 years. 6 years back , the father's age was 2 years more than 4 times the age of the son at that time. Find their present ages?

Answer 1

present age:
let the age of father be x yr
let the age of son be y years
given: x+y=54 ----1st equation
6 yrs back:
fathers age=x-6
sons age = y-6
given: x-6=4(y-6)+2
---> x-6=4y-22
--->x-4y= -16 -----2 nd equation
by solving 1st and 2nd equations,
we get y=14 years
and  x= 40 years.
 hence the age of son and father are 14 and 40 years respectively. 

Answer 2

Answer :
     Let Present age of Father (in Years)= x
       and  Present age of Son (in Years)= y
According to Question,
   x + y = 54
or x = 54 - y  ---- 1st
 Before 6 years ,
       Fathers age = x+6
     Sons Age = y+6
      
       x -6 = 4(y -6) + 2
     or x  - 6 = 4y - 24 + 2
         x  = 4y  - 22 + 6
         x = 4y - 16 
   Using Ist , we get
     54 - y = 4y - 16
       54 + 16 = 4y + y
     70 = 5y
   or y = 14
Substitute Value of y in Ist we get ,
           x = 54 - 14
           x = 40
      
   Hence Present age of Father = 40 years
and Present age of Son = 14 years

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