Question

Amit was driving in New Town, where all roads either north - south or east - west forming a grid. Roads were at a distance of 1 km from each other in parallel.
Amit started at the intersection of streets no. 7 and 8. He drove 3 km north, 3 km west and 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

Answer 1

The Correct Option is B

Amit's starting point is at the intersection of streets no. 7 and 8, denoted as (7,8). Considering the grid as a coordinate system where moving north increases the y-coordinate and east increases the x-coordinate:

1. Initial Position: (7,8) 
2. 3 km North: Moving north increases the y-coordinate by 3: (7,8) → (7,11)
3. 3 km West: Moving west decreases the x-coordinate by 3: (7,11) → (4,11)
4. 4 km South: Moving south decreases the y-coordinate by 4: (4,11) → (4,7)

From the current position, (4,7), we need a route to return to the starting point (7,8).

• Option I: 3 km East, 2 km South
  Adjustment:
  • 3 km East: increase x by 3: (4,7) → (7,7)
  • 2 km South: decrease y by 2: (7,7) → (7,5)
• Option II: 1 km North, 3 km East
  Adjustment:
  • 1 km North: increase y by 1: (4,7) → (4,8)
  • 3 km East: increase x by 3: (4,8) → (7,8)
• Option III: 1 km North, 2 km West
  Adjustment:
  • 1 km North: increase y by 1: (4,7) → (4,8)
  • 2 km West: decrease x by 2: (4,8) → (2,8)

The only route that brings Amit back to his starting point (7,8) is II only.