Ram walks 3 km towards the east, then turns left and walks 1 km, then turns left again and walks 2 km and finally turns left once more and walks 1 km. How far is he from his starting point?

Difficulty: Easy

Correct Answer: 1 km

Explanation:


Introduction / Context:
This problem is a basic direction sense question involving right angles and short distances in a grid like path. Ram makes three left turns and walks different distances. We are asked for his straight line distance from the starting point after completing all legs of the journey. Such questions test the ability to track relative positions and use simple geometry without getting confused by the wording.


Given Data / Assumptions:
- Ram begins at a starting point that we treat as the origin. - He walks 3 km towards the east. - He then turns left, which from east means turning towards the north, and walks 1 km. - He then turns left again, which from north means turning towards the west, and walks 2 km. - Finally he turns left once more, which from west means turning towards the south, and walks 1 km. - Directions follow the usual compass convention on a flat plane.


Concept / Approach:
The most direct method is to track Ram's coordinates step by step. We consider east as the positive x direction and north as the positive y direction. Each movement changes either x or y because all turns are exactly 90 degrees. After all moves, we compare the final coordinates with the origin. The straight line distance from start is simply the absolute difference along the nonzero axis because, in this particular path, he ends on the same east west line as the start.


Step-by-Step Solution:
1. Start at (0, 0). 2. Move 3 km east: new position is (3, 0). 3. Turn left to face north and walk 1 km: new position is (3, 1). 4. Turn left to face west and walk 2 km: new position is (1, 1). 5. Turn left again to face south and walk 1 km: new position is (1, 0). 6. From the origin (0, 0) to (1, 0) the difference is 1 km along the east west axis.


Verification / Alternative check:
Instead of coordinates, imagine the path as a rectangle. Ram first goes 3 km east and 1 km north. Then by going 2 km west and 1 km south he almost returns to his original east west line. At the end he is 1 km east of the starting line and back at the same north south level as the origin. A quick sketch of the path shows that his final position is exactly 1 km to the east of the starting point. This confirms the coordinate based calculation.


Why Other Options Are Wrong:
- 2 km would result from mistakenly subtracting 3 - 1 - 2 or misreading one of the legs. - 3 km corresponds to the very first leg and ignores all later corrections. - 4 km and 5 km overestimate the distance by adding multiple legs instead of computing net displacement.


Common Pitfalls:
Typical errors include turning in the wrong direction when interpreting "left" or "right", and adding distances walked instead of calculating net displacement. Learners may also forget that returning along a similar path cancels some earlier movement. Drawing a simple diagram with arrows after each instruction is an effective way to avoid these mistakes and to cross check mental calculations.


Final Answer:
Ram is 1 km away from his starting point, directly to the east.

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