Correct Option (3)
The total number of persons in the queue is 48.
- Mr. X is positioned 14th from the front.
- Mr. Y is positioned 17th from the end. To determine Mr. Y's position from the front, the calculation is: 48 (total persons) - 17 (position from end) + 1 = 32. Thus, Mr. Y is 32nd from the front.
- Mr. Z is located exactly in between Mr. X and Mr. Y. To ascertain Mr. Z's position from the front, the average of Mr. X's and Mr. Y's positions is taken: (14 + 32) / 2 = 46 / 2 = 23. Therefore, Mr. Z is 23rd from the front.
- The number of persons situated between Mr. X (14th position) and Mr. Z (23rd position) is calculated as: 23 (Mr. Z's position) - 14 (Mr. X's position) - 1 (to exclude Mr. Z himself) = 8.
Consequently, there are 8 persons between Mr. X and Mr. Z.
Incorrect Options:
Options 1 (6), 2 (7), and 4 (9) are incorrect. The accurate determination of the number of persons between Mr. X and Mr. Z, based on their respective positions and Mr. Z's exact midpoint placement, yields a value of 8. These alternative options do not correspond with the precise numerical outcome derived from the problem's conditions.
