Question

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

Answer 1

the present age of the mother is 36

Answer 2

Answer:

Step-by-step explanation:

Let the current age of the son be x.

6 years ago the son was (x - 6) years old.

The mother was :

(x - 6)(x - 6)

Three years later the son will be :

x + 3

And the mother will be :

3(x + 3) = 3x + 9

Age of mother 6 years ago :

x^2 - 12x + 36

Age of mother now :

x^2 - 12x + 36 + 6 = x^2 - 12x + 42

Age of mother 3 years to come.

x^2 - 12x + 42 + 3 = x^2 - 12x + 45

x^2 - 12x + 45 = 3x + 9

x^2 - 15x + 36 = 0

Solving for x:

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

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

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

x = 3 or 12

The son is either 3 years now or 12 years.

3 years does not make sense since 6 years before means the son was not yet born.

So we take 12 years.

The mother is :

12 × 12 - 12 × 12 + 42

= 42 years old

Their ages now :

Son 12 years old and mother is 42 years old.