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?
(In reply to
answer by K Sengupta)
Let a(1) and b(1) correspond to Albert and Bertrand's current ages.
Their ages were a(2) and b(2) when Albert was precisely half of Bertrand's age.
By the problem:
b(1) - 3a(1)/4 = a(1)/4 + {6*b(2) - 30}/2
=> b(1) - a(1) = 3*b(2)-15 = b(2)-a(2)
Also, 2a(2)=b(2)=t(say)
Therefore, {a(2), b(2)} = (t/2, t)
Then, 3b(2)-15 = b(2) - a(2) gives:
3t-15=t/2, so that:
5t/2=15,
or, t =6
Therefore, a(2)=3, and b(2)=6, so that:
a(1)-b(1)= a(2)-b(2)=3
Accordingly, Bertrand is precisely 3 years older than Albert.
The last time they met, both the ages of Albert and Bertramd were prime numbers. This is only possible if they were respectively 2 and 5.
Consequently, the respective ages of Albert and Bertrand the last time they met was 2 and 5.
explanation to puzzle answer
