From her house Rimi goes 20 km to the north, then 15 km to the west, then 10 km to the south and finally 15 km to the east. In which direction is she from her house now?

Introduction / Context:
This problem asks about the final direction of Rimi from her house after she walks in four straight legs in cardinal directions. The focus is on net displacement, not on the total distance she travels. This is a common type of reasoning question that trains candidates to combine movements along north south and east west axes.

Given Data / Assumptions:
- Rimi starts from her house, treated as the origin. - She moves 20 km towards the north. - Then she turns and moves 15 km towards the west. - Then she moves 10 km towards the south. - Finally she moves 15 km towards the east. - Directions are standard compass directions on a flat plane.

Concept / Approach:
Because all movements are along cardinal directions, we can treat them as changes in horizontal and vertical coordinates. The key idea is that movements in opposite directions partially or fully cancel each other. We therefore compute net movement in the north south axis and in the east west axis. The nonzero net component determines the final direction with respect to the starting point.

Step-by-Step Solution:
1. Start at coordinate (0, 0). 2. Move 20 km north: position becomes (0, 20). 3. Move 15 km west: position becomes (-15, 20). 4. Move 10 km south: position becomes (-15, 10). 5. Move 15 km east: position becomes (0, 10). 6. Comparing (0, 10) with (0, 0), she is 10 km north of the starting point with no east west displacement.

Verification / Alternative check:
We can verify quickly by separate totals. Vertically, total northward movement is 20 km and total southward movement is 10 km, leaving 10 km net to the north. Horizontally, 15 km west and 15 km east cancel completely, giving zero net horizontal movement. A rough sketch as a rectangle up 20, left 15, down 10 and right 15 shows that the path ends directly above the starting position on the same vertical line. This confirms that Rimi is simply to the north of her house.

Why Other Options Are Wrong:
- South is incorrect because the northward travel is greater than the southward travel. - East and West are wrong because the 15 km west and 15 km east completely cancel. - South East would imply a downward and rightward shift, which does not happen here.

Common Pitfalls:
A common mistake is to add all distances and then try to infer a direction, instead of computing net movement along each axis. Another error is forgetting that equal distances in opposite horizontal directions cancel each other. Staying organized by writing separate sums for north and south, and for east and west, makes these problems straightforward even under exam pressure.

Final Answer:
Rimi is to the north of her house after completing the described path.