A person X was driving in a place where all roads ran either north-south or east-west, forming a grid. Roads are at a distance of 1 km from each other in a parallel. He started at the intersection of two roads, drove 3 km north, 3 km west and 4 km south. Which further route could bring him back to his starting point, if the same route is not repeated ?

The correct option is 3 km east, then 1 km north.

Let us trace the driver's path step-by-step on a standard Cartesian coordinate plane, where the starting point is at the origin $(0,0)$. Let the positive y-axis represent North, negative y-axis represent South, positive x-axis represent East, and negative x-axis represent West.

1. Starting point: $(x_0,y_0)=(0,0)$
2. Drive 3 km north: Going North increases the y-coordinate by 3.
New Position: $(0,0+3)=(0,3)$
3. Drive 3 km west: Going West decreases the x-coordinate by 3.
New Position: $(0-3,3)=(-3,3)$
4. Drive 4 km south: Going South decreases the y-coordinate by 4.
Current Position: $(-3,3-4)=(-3,-1)$

To return to the starting point $(0,0)$ from the current position $(-3,-1)$, the driver needs to adjust their coordinates as follows:

- Change in x-coordinate: From $-3$ to $0$, which is an increase of 3 (moving 3 km East).
- Change in y-coordinate: From $-1$ to $0$, which is an increase of 1 (moving 1 km North).

Therefore, driving 3 km east, then 1 km north will bring him directly back to his starting point.