Question

6 years before the age of mother was equal to the square of her son's .3 year hence her age will be thrice the age of her son then find the present ages of the mother and son

Answer 1

HEY Buddy....!! here is ur answer

Answer : 42 years and 12 years.

Let, the present age of mother and her son are x and y respectively.

Given that : 6 years ago the age of mother was equal to square of her son's age and 3 years hence her age will be thrice the age of her son.

According to the question :

$(x - 6) = {(y - 6)}^{2} ......(1) \\ \\ (x + 3) = 3(y + 3)....(2)$

On solving equations :

From equation (2)

$x = 3y + 6$

On putting the value of x in equation (1)

$(3y + 6 - 6) = {(y - 6)}^{2} \\ \\ \\ = > 3y = {y}^{2} - 12y + 36 \\ \\ = > {y}^{2} - 15y + 36 = 0 \\ \\ = > {y}^{2} - 12y - 3y + 36 = 0 \\ \\ = > y(y - 12) - 3(y - 12) = 0 = \\ \\ = > (y - 3)(y - 12) = 0$

Required value of y = 12 and 3 but according to the question the value of y = 3 doesn't exist.

So, the value of y ( present age of son) will be 12 years.

Now, putting the value of x in equation (2)

$x = 3 \times 12 + 6 \\ \\ = > x = 42$

So, the present age of mother will be 42 years.

I hope it will be helpful for you...!!

THANK YOU ✌️✌️