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?