A pilot takes off from a point and flies 35 km towards the west, then turns towards the south and flies 15 km, then turns to the left and flies 20 km, and finally turns towards the north and flies 15 km. After completing these legs of the journey, where is the plane now with respect to its starting position, in terms of direction and distance?

Introduction / Context:
This direction sense problem simulates the flight path of a plane making rectangular turns. The goal is to determine the net displacement of the plane from its starting location, not the total distance flown. It tests whether you can correctly interpret left turns from different directions and then combine east west and north south movements correctly.

Given Data / Assumptions:

• The plane first flies 35 km towards the west.
• It then turns south and flies 15 km.
• Next, it turns to its left and flies 20 km.
• Finally, it turns towards the north and flies 15 km.
• The left turn in the third step is taken from the current direction at that instant.
• All flights occur in a horizontal plane and follow straight line segments.

Concept / Approach:
We apply a coordinate based approach. West and east movements modify the horizontal coordinate, while north and south movements modify the vertical coordinate. Turning left from south leads to east, while turning left from east would lead to north, and so on. We compute each leg in sequence to obtain the final coordinates, then compare with the origin to get the net displacement and direction.

Step-by-Step Solution:
Step 1: Place the starting point at (0, 0). After flying 35 km west, the plane is at (−35, 0). Step 2: It then turns south and flies 15 km, reaching (−35, −15). Step 3: At this point the plane is facing south. A left turn from south makes it face east. It then flies 20 km east, which increases the horizontal coordinate from −35 to −15, giving position (−15, −15). Step 4: Finally, it turns towards the north and flies 15 km. Moving 15 km north raises the vertical coordinate from −15 to 0, so the final position is (−15, 0). Step 5: The starting point is (0, 0). Therefore, the plane is now 15 km to the west of the starting point.

Verification / Alternative check:
Look at the north south movements: 15 km south followed by 15 km north cancel out exactly, leaving no net vertical displacement. For the east west movements, the plane goes 35 km west and then 20 km east. The net displacement is 35 − 20 = 15 km west. There are no other horizontal components. This confirmatory check supports the coordinate calculation.

Why Other Options Are Wrong:
The options 55 km west and 55 km east arise if someone mistakenly adds 35 km and 20 km or mixes direction signs. The option 15 km east reverses the correct net direction, and ignores that the westward leg is longer than the eastward leg. Only 15 km west matches the accurate net movement from the start.

Common Pitfalls:
Errors commonly arise from misinterpreting the left turn from south as going west instead of east, or from forgetting to cancel equal north and south legs. Others mistakenly add distances in opposite directions instead of subtracting. Careful orientation tracking or sketching a diagram makes such puzzles much easier.

Final Answer:
The plane ends up 15 km west of its starting position.