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

Let the mother's age be x years and the son's age be y years

By question,

x - 6 = (y - 6)²

x - 6 = y² - 12y + 36

x = y² - 12y + 42 ---------1

CASE 2

x + 3 = 3(y + 3)

From 1

y² - 12y + 42 + 3 = 3y + 9

y² - 15y + 36 = 0

y² - 12y - 3y + 36 = 0

y(y - 12) -3(y - 12) = 0

y = 3 or y = 12

But if y = 3, y doesn't exist 6 years ago

Thus, y = 12 and x = 42