P and Q start cycling from the same point. P cycles 18 km towards the north and then turns to her right and cycles 3 km. Q cycles 9 km towards the east, then turns towards the north and cycles 10 km, and finally turns left and cycles 6 km. Where is Q now with respect to the final position of P?

Introduction / Context: In this direction sense test, two cyclists P and Q travel along different routes after starting from the same point. The question asks for the location of Q relative to P after both have completed their journeys. This type of problem checks careful tracking of directions, relative displacement, and the ability to convert movements into coordinates.

Given Data / Assumptions:

• P cycles 18 km north from the starting point.
• Then P turns right from facing north and cycles 3 km east.
• Q cycles 9 km east from the starting point.
• Then Q turns north and cycles 10 km.
• Finally, Q turns left from facing north and cycles 6 km west.
• We need the displacement of Q with respect to P.

Concept / Approach: We use a coordinate geometry approach. Take the common starting point as (0, 0). North increases y, south decreases y, east increases x, and west decreases x. After computing the coordinates of P and Q final positions, we subtract P coordinates from Q coordinates to find the relative position of Q with respect to P and then express it as a direction and distance.

Step-by-Step Solution: Start at (0, 0). P cycles 18 km north to reach (0, 18). Facing north, a right turn leads east, so P cycles 3 km east to reach (3, 18). Q cycles 9 km east to reach (9, 0). Then Q cycles 10 km north to reach (9, 10). Facing north, Q turns left and cycles 6 km west to reach (3, 10). Final positions: P at (3, 18) and Q at (3, 10). Relative position of Q from P = (3 - 3, 10 - 18) = (0, -8). Thus, Q is 8 km south of P.

Verification / Alternative check: Notice both P and Q end on the same vertical line x = 3, so there is no east west separation between them. For vertical displacement, P is at y = 18 while Q is at y = 10. Hence, Q is 8 km downwards from P, that is, in the south direction relative to P. This confirms our calculation.

Why Other Options Are Wrong: Option B: 8 km North reverses the actual relative direction. Options C and D: 28 km South or 28 km North substantially overstate the distance and are inconsistent with the path lengths given. Option E: None of these is incorrect because one of the options, 8 km South, exactly matches the correct result.

Common Pitfalls: It is easy to forget that the question asks for Q position with respect to P, not the airport or the origin. Another pitfall is misinterpreting the left turn from north as east instead of west. A simple coordinate diagram keeps the relative orientation clear and helps prevent such mistakes.

Final Answer: Q is located 8 km South of the final position of P.