A paper boy on his cycle first travels 10 km towards the east from his starting point, then turns towards the south and cycles 3 km, then turns towards the west and cycles 6 km, and finally turns to his right and cycles another 3 km. Taking all these movements into account, where is he now with reference to his original starting position in terms of distance and direction?

Introduction / Context:
This question is about direction sense and net position after a series of movements. The paper boy changes direction multiple times and we need to determine where he finishes relative to where he started. It tests the ability to decompose movements into horizontal and vertical components and to understand how right turns affect direction.

Given Data / Assumptions:

• The paper boy cycles 10 km towards the east.
• He then turns south and cycles 3 km.
• Next, he turns west and cycles 6 km.
• Finally, he turns to his right and cycles 3 km.
• Right is defined with respect to his current facing direction.
• All paths are straight and taken on level ground with no elevation changes.

Concept / Approach:
We use a coordinate system based approach. Movements to the east and west only affect the horizontal coordinate, and movements to the north and south only affect the vertical coordinate. The idea is to compute the net east west and net north south displacements separately, and then determine the final position. The last right turn requires careful attention to the direction he is facing at that moment.

Step-by-Step Solution:
Step 1: Assume his starting position is (0, 0). Moving 10 km east shifts him to (10, 0). Step 2: From there he turns south and cycles 3 km, reducing the vertical coordinate. His new position becomes (10, −3). Step 3: Now he turns west and cycles 6 km, reducing the horizontal coordinate by 6. He reaches (10 − 6, −3) which is (4, −3). Step 4: At this point he is facing west. A right turn from west makes him face north. He then cycles 3 km north. Moving north increases the vertical coordinate from −3 to 0, so the final position is (4, 0). Step 5: The starting point is (0, 0), so he ends up 4 km to the east of his starting point and at the same north south level.

Verification / Alternative check:
Look at the net east west displacement: he first goes 10 km east and later 6 km west. The net is 10 − 6 = 4 km east. For north south displacement, he travels 3 km south and then 3 km north, which exactly cancel out, leaving zero net vertical displacement. So his final position must be 4 km east of the start with no north or south offset, which confirms the coordinate calculation.

Why Other Options Are Wrong:
The option 4 km west is opposite to the correctly calculated net eastward displacement. The options 14 km east and 14 km west come from adding distances without cancelling opposite directions and therefore represent total or incorrect path length rather than net displacement. None of them match the actual final position.

Common Pitfalls:
Learners often sum all east and west distances or forget to cancel equal north south movements. Another mistake is misinterpreting the last right turn from west as south instead of north. Keeping a small directional diagram and marking each leg carefully usually prevents these errors.

Final Answer:
The paper boy is finally located 4 km east of his starting position.