There are 4 persons between A and B, and 7 persons between B and C. So, there are four cases possible:

A_ _ _ _ B _ _ _ _ _ _ _ C
B_ _ _ _ A _ _ C
C_ _ _ _ _ _ _ B _ _ _ _ A
C _ _ _ _ A _ _ B

there are 11 persons ahead of C and 13 behind A. As there are more than 11 persons ahead of C in first case depicted above, we can eliminate it. We can proceed with the remaining three cases and eliminate all but second one.

_ _ _B_ _ _ _ A _ _ C _ _ _ _ _ _ _ _ _ _

Minimum possible number of people in the queue = 22.