A person X was driving in a place where all roads ran either north-south or east-west, forming a grid. Roads are at a distance of 1 km from each other in a parallel. He started at the intersection of two roads, drove 3 km north, 3 km west and 4 km south. Which further route could bring him back to his starting point, if the same route is not repeated ?
- (a) 3 km east, then 2 km south
- (b) 3 km east, then 1 km north ✓ UPSC's answer
- (c) 1 km north, then 2 km west
- (d) 3 km south, then 1 km north
Why the answer is (b)
• Take the start as (0, 0), with north as +y and east as +x.
• 3 km north → (0, 3); 3 km west → (–3, 3); 4 km south → (–3, –1).
• To get back to (0, 0) he must go 3 km east and 1 km north.
• Option (b), 3 km east then 1 km north, does exactly this without retracing any part of his route.
• Hence option (b).
Why the other options are wrong
- (a) 3 km east, then 2 km south
- Moving 3 km East and 2 km South from (-3,-1) ends at (0,-3), not the starting point (0,0).
- (c) 1 km north, then 2 km west
- Moving 1 km North and 2 km West from (-3,-1) ends at (-5,0), not the starting point (0,0).
- (d) 3 km south, then 1 km north
- Moving 3 km South and 1 km North from (-3,-1) ends at (-3,-3), not the starting point (0,0).
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.