Kamal starts walking from his home facing the west direction. He walks 10 km towards the west, then takes a right turn and walks another 10 km. He again takes a right turn and walks 10 km to reach his school. How far, in kilometres, and in which direction is his school from his home?

Introduction / Context:
This direction sense question describes Kamal walking a rectangular path. He starts facing west, walks straight, turns right, walks again, turns right once more, and reaches his school. The task is to find the straight line distance and direction from his home to the school. This is a typical problem where the path forms a rectangle and the net displacement is along one side of that rectangle.

Given Data / Assumptions:

• Kamal starts from his home facing west.
• He walks 10 km towards the west.
• He takes a right turn and walks 10 km.
• He takes another right turn and walks 10 km to reach his school.
• He turns at right angles, and there is no diagonal movement.
• We use standard compass directions with perpendicular north south and east west axes.

Concept / Approach:
We model Kamal's motion on a coordinate plane. Moving west from home shifts him along the negative x axis. Turning right from west leads him to face north, and another right from north makes him face east. When he eventually reaches his school, the coordinates of the school relative to the home can be found by summing the horizontal and vertical displacements. The straight line distance is then simply the length of this net displacement and the direction is identified by the sign of the components.

Step-by-Step Solution:
Step 1: Let Kamal's home be at (0, 0).Step 2: Walking 10 km west takes him to (−10, 0). He is now facing west.Step 3: A right turn from west makes him face north. Walking 10 km north takes him to (−10, 10).Step 4: Another right turn from north makes him face east. Walking 10 km east brings him to (0, 10).Step 5: The coordinates of his school are (0, 10) relative to his home at (0, 0).Step 6: The net displacement is 10 km north and 0 km east or west, so the straight line distance is 10 km in the north direction.

Verification / Alternative check:
The path described forms three sides of a rectangle with sides 10 km by 10 km. Kamal starts at one corner, walks along the bottom side to the left, then up the left side, and then along the top side back to the right. This leaves him directly above his starting point, at the opposite corner vertically. Hence the distance from home to school equals the height of the rectangle, which is 10 km, and the direction is straight north. This geometric view agrees with the coordinate reasoning.

Why Other Options Are Wrong:
The option 10 km south would place the school on the opposite side of the home relative to the actual path. The options 20 km north east and 20 km south west grossly overestimate the distance and introduce a diagonal that does not exist in the described path. The option of 0 km would mean he returns exactly to his house, which he does not, because he has only walked three sides of the rectangle, not all four. Only 10 km north matches the net displacement.

Common Pitfalls:
A frequent error is to assume that walking 10 km west followed by two right turns and two more 10 km legs must bring him back home, forgetting that a full loop requires four sides. Another mistake is to mix up right and left turns when facing west or north, which changes the shape of the path. Sketching a rectangle and labelling each leg in order helps make the relative positions of home and school obvious.

Final Answer:
Kamal's school is located 10 km to the North of his home.