Rohan walks a distance of 3 km towards the north, then turns to his left and walks 2 km. He again turns left and walks 3 km. At this point he turns left once more and walks 3 km. How far is he now from the starting point?

Introduction / Context:
This direction sense question describes Rohan walking along a path with several left turns. The sequence of movements forms a polygonal path, and we must determine his final distance from the starting point. The problem is typical of reasoning tests where tracking left and right turns, along with distances, gradually creates a simple geometric shape such as a rectangle or an offset path.

Given Data / Assumptions:

• Rohan walks 3 km towards the north from his starting point.
• He turns left and walks 2 km.
• He again turns left and walks 3 km.
• He then turns left once more and walks 3 km.
• All turns are 90 degrees to the left relative to his current facing direction.
• We are asked only for the straight line distance from his final position to the starting point.

Concept / Approach:
We place Rohan's movements on a coordinate plane to track his position. A left turn is interpreted as a 90 degree anticlockwise rotation from his current direction. With north as positive y and east as positive x, we can represent each leg of the journey as changes in x and y. After the final leg, the straight line distance is the length of the displacement vector from the origin to his final coordinates, which can be found using simple arithmetic rather than full Pythagorean calculation if the components are small.

Step-by-Step Solution:
Step 1: Take the starting point as (0, 0). Rohan initially faces north.Step 2: Walking 3 km north moves him to (0, 3), still facing north.Step 3: A left turn from north makes him face west. Walking 2 km west moves him to (−2, 3).Step 4: A left turn from west makes him face south. Walking 3 km south moves him to (−2, 0).Step 5: A left turn from south makes him face east. Walking 3 km east moves him to (1, 0).Step 6: His final coordinates relative to the starting point are (1, 0).Step 7: The straight line distance from the origin to (1, 0) is simply 1 km.

Verification / Alternative check:
We can also reason geometrically. The first three legs form a rectangle: 3 km up, 2 km left, and 3 km down, bringing him to a point 2 km west of the start along the same horizontal line. The final leg of 3 km east overshoots the starting point by 1 km towards the east, placing him exactly 1 km away from where he began. This visualisation aligns with the coordinate calculation and confirms that the distance is 1 km.

Why Other Options Are Wrong:
The values 5 km and 4 km are much larger than any small offset created by a slight overshoot on the last leg. The option 3 km might be chosen if someone looks only at the first or third leg and ignores the rest of the movement. The value 2 km corresponds to the width of the rectangle created by the second leg, but the additional final leg changes his position further. Only 1 km correctly reflects the net horizontal displacement from the starting point.

Common Pitfalls:
A common error is to assume that because Rohan walked 3 km north and later 3 km south, he must be back at the starting point, forgetting that he shifted west in between. Another mistake is to treat left turns as absolute directions instead of relative to his current facing orientation, which can produce a wrong shape. Drawing a simple diagram or writing coordinates for each step helps prevent these logical slips.

Final Answer:
Rohan is now at a straight line distance of 1 km from his starting point.