Two planes start from the same airport. Plane A flies 50 km towards the east. Plane B flies 15 km towards the north, then turns towards the east and flies 20 km, and then turns to its right and flies 15 km. After these movements, where is plane B located with respect to plane A?

Introduction / Context:
This direction sense question involves relative positions of two planes, each following different routes from the same airport. Rather than asking for each plane absolute distance from the airport, the problem focuses on the position of plane B relative to plane A. Solving this requires tracking movements on a coordinate plane and then comparing the final coordinates of the two planes.

Given Data / Assumptions:

• Both planes start from the same airport.
• Plane A flies 50 km east.
• Plane B flies 15 km north.
• Then B flies 20 km east.
• Then B turns right from facing east and flies 15 km south.
• The directions follow the standard compass orientation.

Concept / Approach:
We represent all positions in an x y coordinate system. Let the airport be at (0, 0). Flying east increases the x coordinate, flying west decreases it, flying north increases the y coordinate, and flying south decreases it. After calculating plane A and plane B final coordinates, we subtract A coordinates from B coordinates to find B displacement relative to A, and then express that result as a direction and distance.

Step-by-Step Solution:
Set the airport at (0, 0). Plane A flies 50 km east to reach (50, 0). Plane B flies 15 km north to reach (0, 15). Then B flies 20 km east to reach (20, 15). Facing east, a right turn leads south, so B flies 15 km south to reach (20, 0). Final positions: A at (50, 0) and B at (20, 0). Relative position of B from A = (20 - 50, 0 - 0) = (-30, 0). Therefore, B is 30 km west of A.

Verification / Alternative check:
Observe that both planes end on the same east west line (same y coordinate). From the airport, A is 50 km east, while B, after going north and then south by equal amounts, ends directly east of the airport by only 20 km. Hence, from A perspective, B lies 30 km back towards the west, confirming our coordinate calculation.

Why Other Options Are Wrong:
Option A: 30 km East reverses the direction relative to A.
Option B and Option D: 70 km East or West are not supported by any realistic difference based on the routes.
Option E: None of these is incorrect because 30 km West is a correct option and matches the calculated displacement.

Common Pitfalls:
A typical mistake is to compare each plane only with the airport and then misread the relative offset, or to forget that the 15 km north and 15 km south legs of B cancel vertically. Another common error is reversing the direction when computing B relative to A. Carefully subtracting coordinates in the correct order avoids such confusion.

Final Answer:
Plane B is located 30 km West of plane A.