Two friends X and Y start running and they run together for 50 m in the same direction and reach a point. X turns right and runs 60 m, while Y turns left and runs 40 m. Then X turns left and runs 50 m and stops, while Y turns right and runs 50 m and then stops. How far are the two friends from each other now?
- (a) 100 m ✓ UPSC's answer
- (b) 90 m
- (c) 60 m
- (d) 50 m
Why the answer is (a)
• Start at (0,0) and move 50 m east to (50,0).
• X turns right (south) 60 m to (50,-60), then left (east) 50 m to (100,-60).
• Y turns left (north) 40 m to (50,40), then right (east) 50 m to (100,40).
• Both final points have x-coordinate 100, so separation is |40 - (-60)| = 100 m.
• Therefore the correct option is (a) 100 m.
Why the other options are wrong
- (b) 90 m
- 90 m is not the vertical gap because the final points are 40 m north and 60 m south of the common 50 m point, giving 100 m.
- (c) 60 m
- 60 m is only X's first turn distance, not the total separation between the final points.
- (d) 50 m
- 50 m is the length of the initial common run and each final leg, not the distance between the final points.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.