Three persons A, B and C are standing in a queue not necessarily in the same order. There are 4 persons between A and B, and 7 persons between B and C. If there are 11 persons ahead of C and 13 behind A, what could be the minimum number of persons in the queue?

The correct option is 22.

To find the minimum number of persons in the queue, we need to arrange the positions of A, B, and C such that they overlap as much as possible, satisfying all the given conditions.

Let us define the positions of the individuals in the queue from front to back, where position 1 is the front-most position.
We are given the following conditions:
1. There are 4 persons between A and B.
2. There are 7 persons between B and C.
3. There are 11 persons ahead of C (meaning C is at position 12).
4. There are 13 persons behind A.

Since we want to minimize the total number of persons, C (who has 11 persons ahead of him) should be placed as far back in the relative order of A, B, and C as possible, while keeping A and B closer to the front. Let us try the arrangement where A is ahead of B, and B is ahead of C. That is, the order from front to back is A, then B, then C.

Let C be at position 12 (since there are 11 persons ahead of C).
If B is ahead of C with 7 persons between them, the position of B is calculated as:
Position of B = Position of C - 7 - 1 = 12 - 8 = 4.
Since Position of B = 4, there are 3 persons ahead of B, which is consistent with C having 11 persons ahead of him.

Now, there are 4 persons between A and B. Since we want to minimize the queue size and A has 13 persons behind him, let us place A ahead of B:
Position of A = Position of B - 4 - 1 = 4 - 5 = -1.
Since a position cannot be negative, A must be behind B. Let's place A behind B:
Position of A = Position of B + 4 + 1 = 4 + 5 = 9.

Let us check if this arrangement works:
- Position of B = 4.
- Position of A = 9.
- Position of C = 12.

Let us verify the conditions for this setup:
1. Persons between A and B: B is at 4, A is at 9. The positions between them are 5, 6, 7, and 8 (4 persons). This condition is satisfied.
2. Persons between B and C: B is at 4, C is at 12. The positions between them are 5, 6, 7, 8, 9, 10, and 11 (7 persons, which includes A at position 9). This condition is satisfied.
3. Persons ahead of C: C is at 12, so there are 11 persons ahead of C (positions 1 to 11). This condition is satisfied.
4. Persons behind A: A is at position 9. We are given that there are 13 persons behind A.

Thus, the total number of persons in the queue is:
Total = Position of A + Number of persons behind A
Total = 9 + 13 = 22.

Since all conditions are satisfied, the minimum number of persons in the queue is 22.