Question

2 years ago a man's age was three times the square of his son's age in 3 years time his age will be 4 times his son's age find their present ages

Answer 1

Hi Mate !!


Let the present age of Son be x
and man be y


• Two years ago their age will be
Son's age :- ( x - 2 )
Man's age :- ( y - 2 )

• 2 years ago a man's age was three times the square of his son's age !!

( y - 2 ) = 3 ( x - 2 )²

y - 2 = 3 ( x² + 4 - 4x )

y - 2 = 3x² + 12 - 12x

3x² - y + 12 + 2 - 12x = 0

3x² - 12x - y + 14 = 0...... ( i )



• After three years their age will be :-
Son's age :- ( x + 3 )
Man's age :- ( y + 3 )


• In 3 years time his age will be 4 times his son's age

( y + 3 ) = 4 ( x + 3 )

y + 3 = 4x + 12

4x - y + 12 - 3 = 0

4x - y + 9 = 0

- y = - 9 - 4x

y = 9 + 4x .... ( ii )

Putting value of y from ( ii ) in ( i )

3x² - 12x - y + 14 = 0

3x² - 12x - 9 - 4x + 14 = 0

3x² - 16x + 5 = 0

3x² - 15x - x + 5 = 0

3x ( x - 5 ) - 1 ( x - 5 ) = 0

( x - 5 ) ( 3x - 1 ) = 0


• ( x - 5 ) = 0

x = 5

• ( 3x - 1 ) = 0

x = 1/3

[ Neglected as bCoz age can't be in fraction ]

So, x = 5

Putting value of x as 5 in eq ( ii )

y = 9 + 4x

y = 9 + 4 × 5

y = 9 + 20

y = 29

So, the present age of son is ( x ) :- 5years

and the present age of man is ( y ) :- 29years.