Brain Teasers
Last Time we Met
Said Alf to Bert, "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". Said Bert to Alf "I'm off down the pub". How old were Alf and Bert the last time they met?
Answer
Alf and Bert were 2 and 5 years old respectively the last time they met. If A and B are Alf and Bert's present ages and a and b are their ages when Alf was half Bert's age thenB - 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, Bert being the older of the two. The father plays no part in the problem!
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