Question

Instructions: Amit was driving in New Town, where all roads run either north-south or east-west, forming a grid. Roads are at a distance of 1 km from each other and are parallel.

Amit started at the intersection of streets no. 7 and 8. He drove 3 km north, 3 km west, and then 4 km south. Which further route could bring him back to his starting point?
I. 3 km east, then 2 km south
II. 1 km north, then 3 km east
III. 1 km north, then 2 km west

• A. I only
• B. II only
• C. I and II only
• D. II and III only

Hint:

Track east-west and north-south distance separately; the return route must bring both back to exactly zero.

Answer 1

The Correct Option is B

Step 1: Set up coordinates.
Take Amit's starting point as (0, 0), with east as the positive x-direction and north as the positive y-direction.

Step 2: Track his position after the first three moves.
3 km north takes him to (0, 3). 3 km west takes him to (-3, 3). 4 km south takes him to (-3, -1). So after these moves, Amit is 3 km west and 1 km south of his starting point.

Step 3: Find what further move cancels this out.
To return to (0, 0) from (-3, -1), he needs a further net movement of +3 in x (3 km east) and +1 in y (1 km north).

Step 4: Test route I.
3 km east, then 2 km south: this adds (+3, -2). New position: \((-3+3,\,-1-2)=(0,-3)\), not the origin, so route I does not work.

Step 5: Test route II.
1 km north, then 3 km east: this adds (+3, +1). New position: \((-3+3,\,-1+1)=(0,0)\), exactly the origin, so route II works.

Step 6: Test route III.
1 km north, then 2 km west: this adds (-2, +1). New position: \((-3-2,\,-1+1)=(-5,0)\), not the origin, so route III does not work.

Step 7: Final Answer.
Only route II brings Amit back to his starting point, so option B is correct.