Shahid and Rohit start from the same point in opposite directions. After each 1 km, Shahid always turns left and Rohit always turns right. Which of the following statements is correct ?
- (a) After both have travelled 2 km, the distance between them is 4 km.
- (b) They meet after each has travelled 3 km. ✓ UPSC's answer
- (c) They meet for the first time after each has travelled 4 km.
- (d) They go on without ever meeting again.
Why the answer is (b)
• Let the starting point be the origin (0,0). Shahid travels North (positive y-axis) and Rohit travels South (negative y-axis) initially.
• After 1 km, Shahid is at (0,1) and Rohit is at (0,-1). Shahid turns left (West) and Rohit turns right (West).
• After the second 1 km (total 2 km), Shahid is at (-1,1) and Rohit is at (-1,-1). They are 2 km apart vertically, so option (a) is incorrect.
• After the third 1 km (total 3 km), Shahid turns left (South) and Rohit turns right (North). Shahid moves from (-1,1) to (-1,0) and Rohit moves from (-1,-1) to (-1,0).
• Both reach the point (-1,0) after travelling exactly 3 km, meaning they meet at this point.
Why the other options are wrong
- (a) After both have travelled 2 km, the distance between them is 4 km.
- After 2 km, Shahid is at (-1,1) and Rohit is at (-1,-1), making the distance between them 2 km, not 4 km.
- (c) They meet for the first time after each has travelled 4 km.
- They meet after 3 km, not 4 km, as their paths intersect at (-1,0) at the 3 km mark.
- (d) They go on without ever meeting again.
- They do meet after 3 km, so the statement that they never meet again is false.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.