A man and his grandson have the same birthday. For six consecutive years, the man's age was a exact multiple of the boy's age. How old were they at the last birthday?

Let the respective ages of the man and his grandson be over the six years be x and (A+x), for x = 1, 2, 3, 4, 5, 6

By the problem x divides (A+x) for x = 1, 2, 3, 4, 5, 6, and accordingly, it follows that:

Min(A) = LCM(1,2,3,4,5,6) = 60

Thus A= 60t. However, we know that, except for very rare cases the age of any human being cannot correspond to 120 years, and therefore, t>=2 is a contradiction.

Thus, substituting (A, x) = (60, 6), we obtain the current ages of the man and his grandson as 6 years and 66 years respectively.

*Edited on ***August 13, 2007, 4:15 am**