RAS question
A man walks 3 km towards South, turns left and walks 4 km, then turns left again and walks 3 km. How far is he from his starting point?
Correct answer: (C) 4 km.
The man is 4 km from his starting point because the 3 km southward and 3 km northward movements cancel each other, leaving a displacement of 4 km east.
Explanation
Start at point O. The man first walks 3 km south. A left turn while facing south makes him face east, so he walks 4 km east. He then turns left again. A left turn while facing east makes him face north, so he walks 3 km north. The 3 km northward movement cancels the initial 3 km southward movement. He therefore finishes exactly 4 km east of O, and his straight-line distance from the starting point is 4 km. NCERT's Learning Outcomes at the Elementary Stage identifies an understanding of distance, direction, location and simple maps as a foundational competency; this question applies that understanding.
Why the other options are wrong
- (A) 5 km results from treating 3 km and 4 km as perpendicular sides of a right triangle, but the final 3 km northward movement cancels the initial 3 km southward movement, leaving only 4 km east.
- (B) 3 km is only the length of each north-south leg. Those two legs cancel each other and do not remain as the final distance.
- (D) 7 km comes from adding only two legs of the route. It is neither the complete path length nor the straight-line distance from the starting point.
Concept
This is a direction-sense and distance question. You must interpret left and right turns from the man's current facing direction and cancel equal movements in opposite directions. Such questions recur in RAS because they test spatial reasoning and careful reading without relying on memorized formulas. The common trap is confusing path length with straight-line distance from the starting point.