Ajay starts from Point A and drives 16 km towards the west. He then takes a right turn, drives 8 km, then turns left and drives 7 km. He then takes a left turn and drives 8 km. He takes a final right turn, drives 2 km, and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90-degrees turns only, unless specified.)

The correct option is 25 km towards east.

Step-by-Step Explanation:

Let us trace Ajay's path step-by-step starting from Point A, using standard cardinal directions (North is UP, South is DOWN, East is RIGHT, West is LEFT):

1. Initial Position: Ajay starts at Point A, which we can take as the origin $(0,0)$.

2. First movement: Drives 16 km towards West.

Position: 16 km West of Point A.

3. Second movement: Takes a right turn (North) and drives 8 km.

Position: 16 km West and 8 km North of Point A.

4. Third movement: Takes a left turn (West) and drives 7 km.

Position: $16+7=23$ km West and 8 km North of Point A.

5. Fourth movement: Takes a left turn (South) and drives 8 km.

Since he was 8 km North and moved 8 km South, his North-South position returns to the horizontal line passing through Point A.

Position: 23 km West of Point A.

6. Fifth movement: Takes a final right turn (West) and drives 2 km, stopping at Point P.

Total distance West from Point A to Point P = $23+2=25$ km.

Position of Point P: 25 km West of Point A.

Determining Direction and Distance to return to Point A:

Since Point P is located 25 km directly to the West of Point A, to reach Point A from Point P, Ajay must drive in the opposite direction (towards the East) for a distance of 25 km.

Therefore, Ajay should drive 25 km towards east to reach Point A again.