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?

Let x be B’s age when he was twice A’s age (when A was half B’s age).

Then the age difference when A was 1/4 his present age (and therefore the constant age difference as that does not change) is (6x-30)/2, or 3x-15. But since difference held also when B was twice A’s age, and B was x years old then, it follows that x=2(3x-15); that is, if B was twice as old as A, then his age was also twice the difference in their ages.

Solving this for x, we get x=6, so the age difference is 3.

In order for two prime numbers to differ by 3, they must be 2 and 5, as 2 is the only even prime.

So the last time they met they were 2 and 5.

Posted by Charlie on 2003-03-02 10:15:14