Question

Shubham starts from Point A and drives 10 km towards south. He then takes a left turn, drives 6 km, turns left and drives 12 km. He then takes a left turn and drives 8 km. He takes a final left 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° turns only unless specified.)

• A. 3 km to the east
• B. 3 km to the west
• C. 2 km to the east
• D. 2 km to the west

Answer 1

Answer:

C. 2 km to the east

1. South Movement: Shubham drives 10 km South from Point A.

2. East Movement: Turning left from South means he heads East for 6 km.

3. North Movement: Turning left again means he goes 12 km North.

   • Mental Check: Since he went 10 km South earlier and now 12 km North, he is currently 2 km north of his starting horizontal baseline.

4. West Movement: Turning left again means he drives 8 km West.

   • Mental Check: He previously went 6 km East. By driving 8 km West, he passes his starting vertical line and ends up 2 km west of it.

5. Final South Movement to Point P: He takes a final left turn (heading South) for 2 km.

   • Mental Check: He was 2 km north of the baseline. Moving 2 km South brings him exactly back onto the starting horizontal line.

Finding the Return Path

• Since the North and South movements completely cancelled each other out, Point P sits exactly on the same horizontal line as Point A.

• Looking at the East/West alignment: He went 6 km East, then 8 km West. This leaves him exactly 2 km to the West of Point A.

Therefore, to get back to Point A from Point P, he needs to drive 2 km towards the East.