Let's track Archana's position on a coordinate grid, with her house at the origin (0, 0). We'll use the x-axis for East-West movement (+East, -West) and the y-axis for North-South movement (+North, -South).

1. Starts at her house: Her initial position is (0, 0).
2. Goes 15 km North: Her new position is (0, 15).
3. Turns left (to face West) and covers 10 km: Her new position is (0 - 10, 15), which is (-10, 15).
4. Turns South and covers 5 km: Her new position is (-10, 15 - 5), which is (-10, 10).
5. Turns left (to face East) and covers 10 km: Her final position is (-10 + 10, 10), which is (0, 10).

Final Direction from Her House

To find her final direction from her house, we compare her starting and ending points:

• Starting Position (House): (0, 0)
• Final Position: (0, 10)

The x-coordinate has returned to 0, meaning there is no net East or West displacement. The y-coordinate is positive, meaning she is 10 km North of her starting point.

Final Answer: She is in the North direction from her house.