Correct Option
To determine the final distance between friends X and Y, we analyze their movements sequentially:
- Both friends start together and run 50 m in the same direction to an intermediate point. This initial common movement does not contribute to their final separation.
- From this intermediate point, X turns right and runs 60 m. Simultaneously, Y turns left and runs 40 m. These movements establish a horizontal separation between them. If we assume the initial common path was North, X moves East for 60 m, and Y moves West for 40 m. The horizontal distance between their current positions is 60 m + 40 m = 100 m.
- Subsequently, X turns left and runs 50 m. If X was moving East, turning left means moving North. Y turns right and runs 50 m. If Y was moving West, turning right means moving North. Both X and Y move 50 m in parallel directions (e.g., North) from their respective positions after the 60 m and 40 m runs.
- Since their final 50 m movements are parallel and in the same relative direction, their vertical displacement from their previous positions is identical. Therefore, their final separation is solely determined by the horizontal distance established after their first divergent turns.
The total distance between X and Y is the sum of the distances they ran in opposite horizontal directions:
Distance = 60 m + 40 m = 100 m
Incorrect Options
Options 2 (90 m), 3 (60 m), and 4 (50 m) are incorrect because they do not accurately account for the cumulative horizontal displacement between X and Y. The final separation is the sum of the distances covered by X and Y after their initial divergence, as their subsequent movements are parallel and do not alter their relative horizontal positions.