Question

Varun starts from Point A and drives 37 km towards the north. He then takes a right turn, drives 39 km, turns right and drives 40 km. He then takes a right turn and drives 45 km. He takes a final right turn, drives 3 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. 5 km to the east
• B. 6 km to the east
• C. 6 km to the west
• D. 5 km to the west

Answer 1

Answer:

B. 6 km to the east

1. North: Varun drives 37 km North from Point A.

2. East: He turns right and goes 39 km East.

3. South: He turns right and goes 40 km South.

   • Comparison: Since he went 37 km North and then 40 km South, he is now 3 km further South than his starting level at Point A.

4. West: He turns right and goes 45 km West.

   • Comparison: He previously went 39 km East. By going 45 km West, he passes Point A's vertical line and ends up 6 km to the West of it 45 - 39 = 6

5. North: He turns right one last time and goes 3 km North to reach Point P.

   • Comparison: He was 3 km South of Point A's level. Going 3 km North brings him perfectly back to the same horizontal line (level) as Point A.

---

Visualizing the Final Position:

• Vertically, he is back on the exact same line as Point A because the 3 km North perfectly balances out the 3 km South deficit.

• Horizontally, he is sitting exactly 6 km to the West of Point A.

Conclusion:

To return to Point A from Point P, he must drive directly opposite to where he is sitting: 6 km towards the East.