A plane flies 100 km towards the west, then turns towards the south and flies 150 km, then turns again towards the west and flies 300 km, and finally turns to its right and flies 150 km. Where is the plane now with reference to its starting position?

Introduction / Context:
This question is another example of a multi step direction sense problem, but using a plane instead of a person. The distances are larger, yet the underlying reasoning is the same. We need to track movements along cardinal directions, account for turns, and finally express the net displacement from the origin in a simple direction and distance form. These skills are widely tested in reasoning sections where spatial tracking is important.

Given Data / Assumptions:

• The plane starts from a fixed reference point.
• First it flies 100 km towards the west.
• Then it turns towards the south and flies 150 km.
• Next it turns towards the west again and flies 300 km.
• Finally it turns to its right and flies 150 km.
• The earth is treated locally as flat, with movements arranged as straight segments and turns of ninety degrees.

Concept / Approach:
We use the coordinate method that is standard for direction sense problems. The starting point is taken as (0, 0). West corresponds to negative x, east to positive x, north to positive y and south to negative y. We compute the plane's coordinates after each leg of the journey and then compare the final coordinates with the origin. Since the last move is back towards the north, some vertical displacement cancels out, and we only need to keep track of what remains horizontally and vertically.

Step-by-Step Solution:
Step 1: Start with the plane at (0, 0).Step 2: It flies 100 km west, so the new position is (-100, 0).Step 3: It then turns south and flies 150 km, which makes the position (-100, -150).Step 4: The plane now turns west again and flies 300 km more. This moves it to (-400, -150).Step 5: Finally, it turns to its right. When facing west, a right turn leads to facing north. Flying 150 km north takes the plane from (-400, -150) to (-400, 0).Step 6: The starting point was (0, 0) while the final point is (-400, 0). Therefore, the plane is 400 km to the west of its starting position and at the same north south level.

Verification / Alternative check:
We can separate horizontal and vertical components. Horizontally, the plane moves 100 km west first and 300 km west later, which gives a total of 400 km west. There is no eastward movement at any stage. Vertically, it flies 150 km south and later 150 km north, so the vertical displacement is zero. Thus the net displacement is purely horizontal: 400 km to the west. This quick summary confirms the coordinate result and rules out any error in sign or cancellation.

Why Other Options Are Wrong:
Option B (200 km West) underestimates the total horizontal movement by combining only a part of the path. Options A and D (400 km East and 200 km East) reverse the direction, which contradicts the repeated westward flights. Only option C correctly states that the plane ends up 400 km west of the starting point, which matches the resultant displacement from our calculation.

Common Pitfalls:
One frequent error is to forget that the final northward movement cancels the earlier southward movement. Candidates sometimes add all distances linearly without recognising direction changes, which leads to an incorrect combined distance. Another pitfall comes from misinterpreting the final right turn from west, sometimes assumed to lead south instead of north. A small sketch with labelled arrows helps avoid these confusions.

Final Answer:
The plane is finally positioned 400 km to the west of its starting point, so the correct option is “400 km West”.