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Age Difference (Posted on 2003-03-02) Difficulty: 3 of 5
Said Albert to Bertrand, "The last time we met, our ages were both prime numbers, and when I was a quarter of the age I am now, you were that age plus half the age your father would have been thirty years previous to when he was six times the age you would have been when I was half your age".

How old were Albert and Bertrand the last time they met?

  Submitted by Ravi Raja    
Rating: 3.5556 (9 votes)
Solution: (Hide)
Albert and Bertrand were 2 and 5 years old repectively the last time they met.
If A and B are Albert's and Bertrand's present ages and a and b are their ages when Albert was half Bertrand's age then
B - 3A/4 = (A/4) + (6b - 30)/2
Since their ages have always had the same difference we have
B - A = 3b - 15 = b - a
and since 2a = b then a = 3 and b = 6.
So their ages differ by 3. Since all primes except 2 are odd and differ by an even number we can only have 2 and 5, Bertrand being the older of the two.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: the text vs reason Ady TZIDON2014-11-25 17:23:12
re: the text vs reason Ady TZIDON2014-11-25 17:23:12
answerK Sengupta2007-11-29 05:01:23
re: Solution attemptx2003-04-29 00:14:06
SolutionSolution attemptDJ2003-03-03 15:53:24
SolutionSolutionCharlie2003-03-02 10:15:14
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