Question

Ten years ago theage of a father was four times of his son ten years hence the age of the father will be twice that of his son the present age of the father and the son is

Answer 1

Let present age of father be X years and Present age of son be Y years.




Before 10 years age of father = ( X - 10 ) years.


And,


Before 10 years age of son = ( Y - 10 ) years.


According to the question,





( X - 10 ) = 4 ( Y - 10 )


X - 10 = 4Y - 40




X - 4Y = -30 -----------(1)




After 10 Years age of father = ( X + 10 ) years.


And,


After 10 Years age of son = ( Y + 10 ) years.



( X + 10 ) = 2 ( Y + 10 )


X + 10 = 2Y + 20


X - 2Y = 10 -----------(2)



From equation (1) , we get

X - 4Y = -30



X = ( -30 + 4Y ) ----------(3)



Putting the value of X in equation (2) , we get




X - 2Y = 10





-30 + 4Y - 2Y = 10



2Y = 40



Y = 20 years.



Putting the value of Y in equation (3), we get




X = ( -30 + 4Y ) = ( -30 + 4 × 20 )


X = 50 years.



Hence,


Present age of father = X = 50 years.


And,


Present age of son = Y = 20 years.

Answer 2

Suppose age of father and son is x and y Years.

a/q,

x - 10 = 4 ( y -10 )

x - 10 = 4y - 40

x-4y = -30 ---(1)

and,

x +10 = 2(y+10 )

x + 10 = 2y + 20

x - 2y = 10 ----(2)

on solving (1) and (2) , we get

x = 50 years and y = 20 years.