Aman drives 5 km from point A towards the south. He then takes a left turn and drives 5 km. He then takes a right turn and drives 5 km. He again takes a right turn and drives 10 km. He finally takes a right turn and drives 10 km to reach 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.)

The correct option is 5 km towards the east.

To find how far and in which direction Aman needs to drive to return from point B back to point A, let us trace his step-by-step movement using Cartesian coordinates (x, y). Let point A be at the origin $(0,0)$, where North is along the positive y-axis, South is along the negative y-axis, East is along the positive x-axis, and West is along the negative x-axis.

Step 1: Start at Point A
Starting coordinates of Point A = $(0,0)$.

Step 2: Drives 5 km towards the South
Moving 5 km south changes the y-coordinate by -5.
Position 1 = $(0,-5)$.

Step 3: Takes a left turn and drives 5 km
Facing South, a left turn leads towards East (positive x-direction).
Position 2 = $(0+5,-5)=(5,-5)$.

Step 4: Takes a right turn and drives 5 km
Facing East, a right turn leads towards South (negative y-direction).
Position 3 = $(5,-5-5)=(5,-10)$.

Step 5: Takes a right turn and drives 10 km
Facing South, a right turn leads towards West (negative x-direction).
Position 4 = $(5-10,-10)=(-5,-10)$.

Step 6: Takes a right turn and drives 10 km to reach Point B
Facing West, a right turn leads towards North (positive y-direction).
Position of Point B = $(-5,-10+10)=(-5,0)$.

Step 7: Distance and direction from Point B to Point A
Aman is currently at Point B $(-5,0)$ and wants to reach Point A $(0,0)$.
Difference in x-coordinates = $0-(-5)=5$ km.
Difference in y-coordinates = $0-0=0$ km.

Since Point A is located at $(0,0)$ and Point B is at $(-5,0)$, Aman must drive 5 km towards the East to return to point A.