Starting from his home, a boy rides his bike 8 km towards the west, then takes a left turn and travels 10 km. From there, he turns 180 degrees in the clockwise direction and travels another 16 km. Finally, he takes a right turn and travels 8 km more. How far and in which direction is he now from his original starting position?

Introduction / Context:
This problem describes a boy riding his bike in several legs, making left and right turns and one 180 degree turn. We must determine his final distance and direction from his home, which is his starting point. Direction sense questions like this require both tracking orientation after each turn and summing up the displacements along the north south and east west directions.

Given Data / Assumptions:

• From home, the boy rides 8 km west.
• He then takes a left turn and rides 10 km.
• From this point he turns 180 degrees clockwise and rides another 16 km.
• Finally he takes a right turn and rides 8 km.
• All movements are along straight lines in the cardinal directions, and 180 degrees clockwise reverses his direction.

Concept / Approach:
We start by translating each leg into coordinates. Taking west as negative x, east as positive x, north as positive y, and south as negative y, each movement gives us a change in x and y. Left and right turns are interpreted relative to the direction he is facing at that moment. A 180 degree clockwise turn simply reverses the facing direction. After summing all displacement vectors, we obtain the net displacement from the starting point, whose magnitude and sign determine the final distance and direction.

Step-by-Step Solution:
Step 1: Let the home position be (0, 0). The boy initially faces west.Step 2: Riding 8 km west takes him to (−8, 0), still facing west.Step 3: From facing west, a left turn takes him to face south. Riding 10 km south takes him to (−8, −10).Step 4: A 180 degree clockwise turn from south reverses his direction to north. Riding 16 km north from (−8, −10) moves him to (−8, 6).Step 5: He is now facing north. A right turn from north takes him to face east. Riding 8 km east from (−8, 6) moves him to (0, 6).Step 6: His final coordinates are (0, 6) relative to his home at (0, 0).Step 7: The net displacement is 6 km north and 0 km east or west, so the distance is 6 km and the direction is north.

Verification / Alternative check:
We can check the vertical movements alone: he goes 10 km south and then 16 km north, which gives a net 6 km north. For the horizontal movement, he first goes 8 km west and later 8 km east, which cancel exactly, yielding net 0 km in the east west direction. So even without coordinates, we can see that horizontally he returns to the same line as his starting point, but vertically he ends 6 km north of it. This confirms that the final location is 6 km towards the north of his home.

Why Other Options Are Wrong:
The option 10 km south would require the net vertical displacement to remain negative, which is inconsistent with going 16 km north after 10 km south. The option 12 km west implies an uncancelled 12 km horizontal offset, which is impossible since 8 km west is later countered by 8 km east. The option 6 km east would require a net positive x displacement, but we found the final x coordinate to be zero. The 4 km north west suggestion combines both north and west components and does not fit the exact cancellation of horizontal motion.

Common Pitfalls:
Common mistakes include misinterpreting the 180 degree clockwise turn and thinking it leads to east instead of north, or forgetting to cancel the equal east and west legs of 8 km each. Another error is to compute total distance travelled rather than net displacement. Focusing on net north south and east west components and recognising when movements cancel each other is crucial for accuracy in such problems.

Final Answer:
The boy is now located 6 km to the North of his original starting position at home.