To find the ratio p : q : r, first express p and q in terms of a common variable. From p : q = 3 : 5/6, we can write p = 3k and q = 5k/6 for some k. Next, using q : r = 3 : 1/2, we can express r in terms of q, leading to the combined ratio p : q : r as 12 : 15 : 16 after finding a common multiple.