In a company of Clergymen, Doctors and Lawyers it is found that the sum of the ages of all present is 2160; their average age is 36; the average age of the Clergymen and the Doctors is 39; the average age of the Doctors and the Lawyers is (32 + 8/11); the average age of the Clergymen and the Lawyers is (36 + 2/3).

If each Clergymen had been 2 years older, each Lawyer 5 years older, and each Doctor 7 years older, then the average age of everyone present would have been greater by 5 years.

Determine the number of each profession present and their average ages.