Two motorcyclists P and Q start from the same point. P rides 11 km west, then turns south and rides 16 km, then turns to his right and rides 14 km. Q rides 30 km south, then turns to his right and rides 25 km. Where is Q with respect to P now?

Introduction / Context:
This question tests your understanding of direction sense and relative position in two dimensional space. Two riders move in different directions and distances from the same starting point. You are asked to determine where one rider is located relative to the other at the end of their journeys. Such questions combine basic coordinate geometry ideas with careful reading of directions like north, south, east, and west.

Given Data / Assumptions:
- P starts at the origin point and rides 11 km west, then 16 km south, then 14 km further after turning right from south.
- Q starts at the same origin, rides 30 km south, then turns right and rides 25 km.
- Directions follow the standard convention: north up, south down, east right, west left on an imaginary map.
- We must find Q’s position relative to P, not relative to the original starting point.

Concept / Approach:
A convenient way to solve such problems is to place the starting point at the origin of a coordinate system. We can treat east as the positive x direction, west as negative x, north as positive y, and south as negative y. Then each segment of motion becomes a change in coordinates. After computing the final coordinates of P and Q, we subtract them to find the relative displacement of Q from P and interpret that displacement as a direction and distance.

Step-by-Step Solution:
Step 1: Let the starting point be (0, 0). West is negative x, south is negative y. Step 2: P rides 11 km west to (-11, 0). Step 3: P then rides 16 km south to (-11, -16). Step 4: From facing south, a right turn leads to west, so P rides 14 km west to (-25, -16). Step 5: Q rides 30 km south from (0, 0) to (0, -30). Step 6: From facing south, Q turns right, which again is towards west, and rides 25 km to (-25, -30).

Verification / Alternative check:
Now compare the coordinates. P ends at (-25, -16) and Q ends at (-25, -30). The x coordinates are equal, so they are vertically aligned. The difference in y is -30 minus (-16) = -14. This means Q is 14 km further south along the same vertical line. Hence, with respect to P, Q is 14 km to the south. The result is consistent with a diagram drawn to scale and with the interpretation of right turns from a southward direction.

Why Other Options Are Wrong:
- Option 14 km North reverses the direction; the calculations clearly show that Q is below P, not above.
- Option 44 km South incorrectly combines distances without paying attention to the actual relative displacement.
- Option 44 km North is both the wrong distance and the wrong direction.

Common Pitfalls:
Students often confuse left and right turns when they imagine the rider facing south or west instead of north. Another typical error is to add distances directly without working through coordinates or drawing a sketch. To avoid these mistakes, always track direction changes step by step and, if needed, sketch the path on paper with axes marked.

Final Answer:
After following their respective routes, Q is located 14 km directly south of P. Therefore, the correct answer is 14 km South.