Step-by-step Solution
1. Analyze the given information:
• There are 5 persons between A and B.
• There are 8 persons between B and C.
• There are 3 persons ahead of C.
• There are 21 persons behind A.
2. Consider the arrangement for minimum persons: To minimize the total number of persons, an overlapping arrangement of A, B, and C is considered. The arrangement where C is first, followed by A, and then B, allows for the most overlap.
3. Determine the position of A relative to C:
• There are 3 persons ahead of C.
• There are 8 persons between B and C.
• There are 5 persons between A and B.
• If C is ahead of B, and A is between C and B, then the number of persons between C and A can be calculated.
• The number of persons between C and A is found by subtracting the persons between A and B from the persons between C and B: 8−5−1=2 (where 1 accounts for person A being between C and B).
• Therefore, there are 2 persons between C and A.
4. Calculate the total number of persons:
• The number of persons ahead of C is 3.
• Person C is 1.
• The number of persons between C and A is 2.
• Person A is 1.
• The number of persons behind A is 21.
• The total number of persons in the queue is the sum of these values: 3+1+2+1+21=28.
Final Answer
The minimum number of persons in the queue is 28.
