Three persons A, B and C are standing in a queue. There are five persons between A and B and eight persons between B and C. If there are three persons ahead of C and 21 persons behind A, what is the minimum possible number of persons in the queue?

Introduction / Context:
This is a more challenging queue and ranking question involving three people and several conditions about how many people stand between them and at the ends of the queue. You must translate the verbal description into positions on a line, then deduce the minimum total number of persons that can satisfy all constraints. Such problems test systematic reasoning and careful handling of distances.

Given Data / Assumptions:

- There are five persons between A and B.- There are eight persons between B and C.- There are three persons ahead of C in the queue.- There are 21 persons behind A.- We want the minimum possible number of persons in the queue that satisfies all these conditions.

Concept / Approach:
First, convert the statements about persons between A, B and C into equations relating their positions. If there are k persons between two people, their position numbers differ by k + 1. We then place C using the information about three persons ahead of C. After that, we place A using the information about persons behind A. By trying both possible orders of A and B around C and satisfying the distance constraints, we determine the total number and select the minimum that works.

Step-by-Step Solution:
Step 1: Let the queue be numbered from front to back starting at 1.Step 2: Three persons ahead of C means C is at position 4.Step 3: There are 21 persons behind A, so if the total number of persons is N, then A is at position N - 21.Step 4: There are five persons between A and B, so the positions of A and B differ by 6. So either B = A + 6 or B = A - 6.Step 5: There are eight persons between B and C, so the positions of B and C differ by 9. Since C is at position 4, B must be at 4 + 9 = 13 or 4 - 9, which is negative and impossible. Thus, B is at position 13.Step 6: With B at 13 and five persons between A and B, A can be at position 13 - 6 = 7 or 13 + 6 = 19.Step 7: A must also satisfy A = N - 21. If A is at 7, then N = 7 + 21 = 28. If A is at 19, then N = 19 + 21 = 40.Step 8: Both N = 28 and N = 40 satisfy the positional relationships, but the question asks for the minimum possible number of persons, so we choose N = 28.

Verification / Alternative check:
For N = 28, positions are: C at 4, B at 13 and A at 7. There are three persons ahead of C (positions 1, 2 and 3), five persons between A and B (positions 8 to 12), eight persons between B and C (positions 5 to 12), and 21 persons behind A (positions 8 to 28). All conditions are satisfied with N = 28, confirming it is valid and minimal.

Why Other Options Are Wrong:
Options 40 and 41 involve higher possible totals. Although N = 40 also works, the question explicitly asks for the minimum possible number, so 40 and 41 are too large. Option 27 is too small to accommodate the required gaps between A, B and C along with the persons ahead of C and behind A. Thus, only 28 is both feasible and minimal.

Common Pitfalls:
Students often forget to check both possible positions for A around B, or they ignore the requirement to find the minimum total. Some also misinterpret phrases like persons ahead and persons behind, confusing them with positions from the given end. Drawing a rough sketch of the queue can greatly reduce such errors.

Final Answer:
The minimum possible number of persons in the queue is 28.