Preethi walks 2 km East for 20 minutes.  Then she turns right and runs 3 km South in 10 minutes.  Then she again turns and walks 2 km West for 30 minutes.

To analyze Preethi's movements, we can break down her journey step by step, keeping track of her position using a coordinate system where East is positive x-direction, North is positive y-direction, West is negative x-direction, and South is negative y-direction.

1. Preethi's Initial Position

Let's assume Preethi starts at the origin:

• Initial Position: $(0, 0)$

2. Movement 1: Walking East

• Preethi walks 2 km East.
• New Position: $(0 + 2, 0) = (2, 0)$

3. Movement 2: Turning Right and Running South

• Preethi turns right (now facing South) and runs 3 km South.
• New Position: $(2, 0 + (-3)) = (2, -3)$

4. Movement 3: Turning Again and Walking West

• Finally, Preethi turns again (now facing West) and walks 2 km.
• New Position: $(2 - 2, -3) = (0, -3)$

5. Final Position and Summary

At the end of her journey, Preethi's final position is: $\mathbf{Final\ Position:\ (0, -3)}$

Final Answer

Preethi ends up at the coordinate $(0, -3)$.