Question

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

Answer 1

$\bold{\boxed{Solution:}}$

Let present age of father = x

and present age of son = y

$\bold{\boxed{A.T.Q}}$

↪Two years ago,

x - 2 = 3(y - 2)^2..............1

↪Three years hence,

x + 3 = 4(y + 3) ............2

Now, from equation 2,

x = 4(y + 3) - 3

From equation 1,

=> 4(y + 3) - 3 - 2 = 3(y - 2)^2

=> 4y + 12 - 5 = 3(y -2)^2+ 4 - 4y)

=> 4y + 7 = 3y^2+ 12 - 12y

=> 3y^2+ 12 - 12y - 4y - 7 = 0

=> 3y^2- 16y + 5 = 0

=> (y - 5) × (3y - 1) = 0

=> y= 5, $\frac{1}{3}$

Since age can not be in fraction,

So y = 5

From equation 2,

 ▶   x + 3 = 4(5 + 3)

=> x + 3 = 4*8

=> x + 3 = 32

=> x = 32 - 3

=> x = 29

So, present age of father = 29

and present age of son = 5

$\bold{\boxed{Thank you!!}}$