Two motorcycle riders, A and B, start from the same point. Rider A rides 11 km towards the east and then turns to his right and rides another 9 km. Rider B rides 8 km towards the north, then turns towards the east and rides 11 km, and finally turns to his right and rides 7 km. Where is rider A with respect to rider B?

Introduction / Context:
This question asks about the relative position of two moving objects, both starting from the same point but following different routes. It checks whether the student can track two paths simultaneously and then compare their final positions. Such problems combine the basic direction sense technique with relative displacement, which is a very common pattern in reasoning sections of competitive exams.

Given Data / Assumptions:

• Rider A starts from the common origin and goes 11 km east.
• Then rider A turns to his right and travels 9 km.
• Rider B also starts from the same origin and goes 8 km north.
• Rider B then turns east and travels 11 km.
• Finally, rider B turns to his right and travels 7 km.
• All paths are straight and all turns are at right angles.

Concept / Approach:
We use a simple coordinate based approach. Place the common starting point at (0, 0). East is taken as positive x, west as negative x, north as positive y and south as negative y. Calculate the final coordinates of rider A and rider B separately. Once we have both positions, we subtract to find the displacement of A relative to B, which tells us in which direction and how far A is from B.

Step-by-Step Solution:
Step 1: For rider A, start at (0, 0). Move 11 km east to (11, 0).Step 2: Facing east, a right turn means facing south. Riding 9 km south changes the position to (11, -9).Step 3: For rider B, begin at the same origin (0, 0). Move 8 km north, reaching (0, 8).Step 4: From there, B turns east and rides 11 km, which moves him to (11, 8).Step 5: B now faces east. A right turn from east means facing south. Travelling 7 km south gives B the final position (11, 1).Step 6: Rider A is at (11, -9) and rider B is at (11, 1). The x coordinates are equal, so both are on the same vertical line. The y coordinate of A is 10 units less than that of B, meaning A is 10 km south of B.

Verification / Alternative check:
We can ignore the first common segment in the east direction for both riders, because ultimately they both shift to the same east coordinate of 11 km. The difference lies only in how far north or south they end up. From the starting point, B effectively goes 8 km north and then 7 km south, ending 1 km north of the origin. A goes no north at all but ends 9 km south. Therefore, A is 10 km south of B, which agrees with the coordinate method and confirms that the calculation is consistent.

Why Other Options Are Wrong:
Option B (8 km South) mistakenly focuses on a partial difference in north south travel. Option C (10 km North) reverses the correct direction. Option D (8 km North) again selects the wrong magnitude and direction. Only option A captures both the correct distance and the correct orientation by stating that rider A is 10 km to the south of rider B.

Common Pitfalls:
Candidates may mix the paths of the two riders or forget that both share the same starting point. Another typical error is to compare each leg individually instead of the final net displacement. Keeping the paths separate, assigning coordinates, and then comparing final positions is the safest and most general method for all such relative position questions.

Final Answer:
Rider A is located 10 km to the south of rider B, so the correct option is “10 km South”.