Sunil drives 5 km from point A towards the west. He then takes a left turn and drives 6 km. He again takes a left turn and drives 11 km. He then takes a left turn and drives 6 km. He finally takes a right turn and drives 6 km to arrive at point B. How much and in which direction does he have to drive to return to point A?
(All the turns are 90° turns only.)

Correct Answer: 12 km towards the west

To determine the distance and direction Sunil must drive to return from point B to point A, we can trace his path step-by-step using a standard Cartesian coordinate system where point A is located at the origin (0, 0).
Let East be along the positive x-axis, West along the negative x-axis, North along the positive y-axis, and South along the negative y-axis.

Step-by-Step Path Analysis:

1. Initial movement from Point A:
Sunil starts at Point A (0, 0) and drives 5 km West.
Position = (-5, 0)

2. First turn:
Facing West, he turns left (facing South) and drives 6 km.
Position = (-5, -6)

3. Second turn:
Facing South, he turns left (facing East) and drives 11 km.
Position = (-5 + 11, -6) = (6, -6)

4. Third turn:
Facing East, he turns left (facing North) and drives 6 km.
Position = (6, -6 + 6) = (6, 0)

5. Final turn to Point B:
Facing North, he turns right (facing East) and drives 6 km to reach Point B.
Position of Point B = (6 + 6, 0) = (12, 0)

Conclusion:
Point B is at coordinate (12, 0), which is 12 km to the east of Point A (0, 0).
To return directly from Point B to Point A, Sunil must travel 12 km in the opposite direction, which is 12 km towards the west.