Question

6 years before the age of mother was equal to the square of her sons age, 3 years hence ,her age will be thrice the age of her son then ,find the present ages of the mother and son ?

Answer 1

Hey.


Here is the answer.


Let the present age of son be x

And mother's age be y.


6 year before :


Mother's age = y - 6

= (x-6)^2 = x^2 + 36 - 12x

or, y = x^2 -12x + 42_________(1)


3 years hence,

Mother's age, y + 3 = 3(x+3) = 3x + 9

so, y = 3x + 6___________(2)


Equating (1) & (2) ;


x^2 -12x + 42 = 3x + 6

or, x^2 -15x + 36 = 0

or, x^2 - 3x - 12x + 36 = 0

or, x ( x -3 ) - 12 ( x - 3 ) = 0

or, ( x-3 ) (x-12) = 0

so, x = 3 , 12

So, son's age can be 3 yr or 12 yr.


and mother's age can be 15 yrs or 42 yrs

So, 3 yrs and 15 yrs are discarded.


Hence, son = 12 yr


Mother = 42 yr.


Thanks