Question

Five years ago, a woman’s age was the square of her son’s age. Ten years later her age will be twice that of her son’s age. Find:
The age of the son five years ago.

Answer 1

Let the age of son be x years five years ago.
∴ Mother's age be x² years five years ago.
After ten years son's age be (x + 15) years and woman's age (x² + 15)
Given x² + 15 = 2(x + 15)
x² + 15 = 2x + 30
x² - 2x - 15 = 0
(x - 5) (x + 3) = 0
x = 5
Or x = -3 (not possible)
∴ Son's age five years ago = 5years.