A and B start from the same point. A cycles 8 km towards the south, then turns to her right and cycles 5 km. B cycles 3 km towards the north, then turns to the west and cycles 5 km, and finally turns to her left and cycles 4 km. After these movements, where is B located with respect to the final position of A?

Introduction / Context:
This problem is a classic direction sense test where two persons, A and B, start from the same point and travel in different directions with several turns. The aim is to determine the final relative position of B with respect to A by tracking their paths systematically on an imaginary grid. It checks careful reading of directions, understanding of right and left from the current facing, and displacement calculation.

Given Data / Assumptions:

• A travels 8 km south from the common starting point.
• Then A turns right from south and cycles 5 km west.
• B travels 3 km north from the starting point.
• Then B turns west and cycles 5 km.
• Finally, B turns left from west and cycles 4 km south.
• Standard north, south, east, west directions are used.

Concept / Approach:
We interpret movements on a coordinate plane. Choose the starting point as (0, 0). For south decrease the y coordinate, for north increase it; for east increase the x coordinate, and for west decrease it. After computing the final coordinates of A and B, we subtract A position from B position to find the relative displacement of B from A and convert this into a direction and distance statement.

Step-by-Step Solution:
Let the start point be O = (0, 0). A moves 8 km south: A1 = (0, -8). Facing south, a right turn leads to west, so A moves 5 km west: A2 = (-5, -8). B moves 3 km north: B1 = (0, 3). Then B turns west and moves 5 km: B2 = (-5, 3). Facing west, a left turn points south, so B moves 4 km south: B3 = (-5, -1). Final positions: A at (-5, -8) and B at (-5, -1). Relative position of B from A = (-5 + 5, -1 + 8) = (0, 7). So B is 7 km due north of A.

Verification / Alternative check:
Draw a simple grid. Both paths end on the same vertical line (same west displacement), but B is clearly higher than A by 7 km. This confirms that B is directly north of A at a distance of 7 km, matching our coordinate calculation.

Why Other Options Are Wrong:
Option B: 7 km South reverses the direction.
Option C and Option D: 15 km North or South exaggerate the distance and are not supported by the movement data.
Option E: None of these is incorrect because we have an exact match in Option A.

Common Pitfalls:
A common mistake is to forget that left and right depend on the current facing direction, not on the page. Another pitfall is mixing up absolute positions with relative positions and comparing each person only to the origin instead of directly comparing A and B positions. Using coordinates or a rough diagram greatly reduces errors.

Final Answer:
B is located 7 km North of the final position of A.