Question

2 years ago, a man’s age was 3 times the square of his son’s age. 3 years hence, his age will be 4 times his son’s age. Find their present ages.

Answer 1

Let the present age of man be y. Hence, his age 2 years ago = (y - 2) yrs.

Let the present age of son be x. Hence, his age 2 years ago = (x - 2) yrs.

According to the question,

$(y-2)=3(x-2{)}^2$ -------------------- 1

After 3 years, man’s age =(y + 3)

After 3 years, son’s age =(x + 3)

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

Solving equation (1) we get:-

$y=3x^2-12x+14$ ------------------- 3

Solving equation (2) we get:-

y = 4x + 9 ---------------------------- 4

Putting the value of y in equation (3) we get

$3x^2-16x+5=0\Rightarrow (3x-1)(x-5)=0$

By solving, we get $x=\frac{1}{3}and5.\frac{1}{3}$ is not considered because it doesn’t fulfill the condition.

$\Rightarrow x=5$. Putting the value of x in equation (2) we get y = 29.

So, present ages of the father and the son are 29 yrs. and 5 yrs. respectively.