Option A: 100 m
Let's break down the movements of X and Y step by step:
     ● Initial Position: Both X and Y start from the same point and run together for 50 m in the same direction.  
     ● Position after 50 m: They reach a common point after running 50 m together.  
     ● X's Movement:  
           ○ X turns right and runs 60 m.
           ○ Then, X turns left and runs 50 m.
     ● Y's Movement:  
           ○ Y turns left and runs 40 m.
           ○ Then, Y turns right and runs 50 m.
     Now, let's visualize their final positions:
     ● X's Final Position:  
           ○ After turning right and running 60 m, X is 60 m perpendicular to the initial direction.
           ○ After turning left and running 50 m, X is now 50 m parallel to the initial direction from the point where X turned right.
     ● Y's Final Position:  
           ○ After turning left and running 40 m, Y is 40 m perpendicular to the initial direction.
           ○ After turning right and running 50 m, Y is now 50 m parallel to the initial direction from the point where Y turned left.
     To find the distance between X and Y, we need to calculate the straight-line distance between their final positions:
     ● Horizontal Distance: Both X and Y have moved 50 m parallel to the initial direction, so the horizontal distance between them is 0 m.  
     ● Vertical Distance: The vertical distance between X and Y is the sum of the perpendicular distances they moved:  
           ○ X moved 60 m perpendicular to the initial direction.
           ○ Y moved 40 m perpendicular to the initial direction.
           ○ Total vertical distance = 60 m + 40 m = 100 m.
     Therefore, the distance between X and Y is the vertical distance, which is 100 m.
     Hence, the correct answer is Option A: 100 m.