Question

The age of a father 8 years ago was 5 times that of his son. 8 years hence his age will be 8 years more than twice the age of his son. Find the present age.

Answer 1

assume that that the age of son (8 years) ago was = x years
hence the age of his father was = 5x
the equation of ages after 8 years from present times =
age of son= x + 8 years + 8 years
= x + 16 years
age of father= 5x + 8 years + 8 years
= 5x + 16 years
balancing the equations-
$5 \: x + 16 = 2(x + 16) + 8 \\ = 5x + 16 = 2x + 32 + 8 \\ = 5x - 2x = 40 - 16 \\ = 3x = 24 \\ = 8$