A boy leaves his school and first travels 8 km towards the east. He then takes a left turn and travels 6 km in that direction, after which he turns towards the east again and travels another 5 km. Finally, he takes a right turn and travels 10 km. In which direction is he now located from his school?

Introduction / Context:
This direction sense problem describes a multi step path taken by a boy leaving his school. We are asked for the direction of his final position as seen from the school. As with many such questions, the key is to track all east west and north south components and then determine which quadrant of the compass the final point lies in relative to the start.

Given Data / Assumptions:

• The boy walks 8 km east from his school.
• He then takes a left turn and walks 6 km in that direction.
• After that he turns towards the east and walks another 5 km.
• Finally, he takes a right turn and walks 10 km.
• Left and right are relative to his current direction, and all turns are right angled turns.
• The ground is flat and all distances are accurate.

Concept / Approach:
We track his path using coordinates. East west movements change the horizontal coordinate, and north south movements change the vertical coordinate. After determining the final coordinates of his position relative to the school, we look at the signs of the horizontal and vertical values to decide whether he is in the North-east, South-east, South-west, or North-west quadrant relative to the school.

Step-by-Step Solution:
Step 1: Set the school at (0, 0). After the boy walks 8 km east, he is at (8, 0). Step 2: From facing east, a left turn makes him face north. He walks 6 km north, so his position becomes (8, 6). Step 3: Next he turns towards the east again, which sets his direction to east, and he walks 5 km. His new position is (8 + 5, 6) = (13, 6). Step 4: Now he is facing east. A right turn from east makes him face south. He then walks 10 km south, reducing the vertical coordinate to 6 − 10 = −4, so his final position is (13, −4). Step 5: The x coordinate is positive and the y coordinate is negative, which means he is to the east and south of the school, that is, in the South-east direction from his school.

Verification / Alternative check:
His net eastward movement is 8 km plus 5 km, totalling 13 km. There is no movement west, so he remains 13 km east of the school. For north south displacement, he moves 6 km north and then 10 km south, giving a net of 4 km south. So from the school as the origin, his final position lies in the South-east quadrant, which confirms the direction as South-east.

Why Other Options Are Wrong:
The option West is incorrect because he clearly has moved net eastward. The option East ignores the fact that he has a net southward component too, so the correct description must mention South-east rather than purely East. The option North-east is not correct because his net vertical displacement is southward, not northward.

Common Pitfalls:
Students often mis-handle the turning instructions, especially when the text says he turns towards a named direction after previously using relative left or right turns. Some also add distances without checking signs, which can produce a mistaken northward displacement. Drawing a simple grid with coordinates helps keep the direction sense accurate.

Final Answer:
The boy is finally located in the South-East direction from his school.