Question

Six year 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

Answer:

12 years, 42 years

Step-by-step explanation:

Let the mother's age = 'x' and Son's age = 'y'.

∴ 6 years before, the age of mother was equal to square of her son's age

⇒ (x - 6) = (y - 6)²

⇒ x - 6 = y² + 36 - 12y

⇒ x = y² + 42 - 12y

Now,

Given that three years hence, her age will be thrice the age of her son.

⇒ x + 3 = 3(y + 3)

⇒ x + 3 = 3y + 9

⇒ x = 3y + 6

⇒ y² + 42 - 12y = 3y + 6

⇒ y² - 15y + 36 = 0

⇒ y² - 12y - 3y + 36 = 0

⇒ y(y - 12) - 3(y - 12) = 0

⇒ (y - 3)(y - 12) = 0

⇒ y = 12,3{Cannot be considered because the age will be negative six years ago}

⇒ y = 12.

when y = 12:

⇒ x = y² + 42 - 12y

      = 144 + 42 - 144

      = 42.

Therefore:

Present age of son = 12 years

Present age of Mother = 42 years