Question

One year ago, a man was 8 times as old as his son. Now, his age is equal to the square of his son’s age. Find their present ages.

Answer 1

Let the present age of the son be x years.

∴ Present age of man = x² years

One year ago,

Son’s age = (x – 1) years

Man’s age = (x² – 1) years

It is given that one year ago; a man was 8 times as old as his son.

∴ (x² – 1) = 8(x – 1)

x² – 8x – 1 + 8 = 0

x² – 8x + 7 = 0

(x – 7)(x – 1) = 0

x = 7, 1

If x = 1, then x² = 1, which is not possible as father’s age cannot be equal to son’s age.

So, x = 7.

Present age of son = x years = 7 years

Present age of man = x² years = 49 years.