Cab driver Bob mentioned to his friend Jim that he recently drove three passengers in his cab, that the product of their (the passengers') ages was 2450, and that the sum of their ages was exactly twice Jim's age.

From this, Jim couldn't deduce what their three ages were.

But when Bob added that he was younger than at least one of the passengers, Jim, who knew Bob's age, was able to deduce all the passengers' ages.

What were Bob's and Jim's ages, and the ages of the passengers?

Assuming that all ages are treated as integers for sums and products (also assuming hacks must be of a certain age -- but not needed): there are ten combinations of three integer ages which give product of 2450. Eight of these give a unique value for Jim's age, so are excluded (since he would then know which combination matched his age). The remaining two give passengers ages as either 5-10-49 or 7-7-50, with sum 64 and Jim's age as 32. If Bob's age (known to Jim) were 49, then the passengers must be 7, 7, and 50, so the answer is 49, 32, 50, 7, 7.