The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find their present ages.

Explanation

Let the present age of the son be x years.
Then, the present age of the man is `(2x^(2))` years.
Age of the son 8 years hence `=(x+8)` years.
Age of the man 8 years hence `(2x^(2)+8)` years.
`:." "(2x^(2)+8)=3(x+8)+4`
`implies" "2x^(2)-3x-20=0implies2x^(2)-8x+5x-20=0`
`implies" "2x(x-4)+5(x-4)=0implies(x-4)=0implies(x-4)(2x+5)=0`
`implies" "x-4=0" or "2x+5=0`
`implies" "x=4" or "x=(-5)/(2)`
`implies" "x=4" "[because" age cannot be negative"].`
`:." ""son's present age = 4 years, and"`
man's present age `=(2xx4^(2))` years = 32 years.