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Ages (Posted on 2004-08-31) Difficulty: 2 of 5
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?

See The Solution Submitted by Federico Kereki    
Rating: 3.0000 (7 votes)

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Solution Puzzle Solution | Comment 8 of 10 |

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
  Posted by K Sengupta on 2007-08-13 03:59:07

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