# 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.

Let the present age of son be x years

The present age of man = x2 years

One year ago age of son = (x – 1)years

age of man = (x2 – 1)years

According to given question, One year ago, a man was 8 times as old as his son

x2 – 1 = 8(x – 1)

x2 – 1 = 8x – 8

x2 – 8x + 7 = 0

x2 – 7x – x + 7 = 0

x(x – 7) – 1(x – 7) = 0

(x – 7) (x – 1) = 0

x = 1 or x = 7

Man’s age cannot be 1 year

Thus x = 7

Thus the present age of son is 7 years

The present age of man is 72 = 49 years

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