Rani went $20\text{km}$ towards west, then turned left and went $20\text{km}$. She again turned left and went $20\text{km}$. She took a $45^{\circ }$ turn towards her left and went straight. In which direction is she walking now?

Let's trace Rani's movements step-by-step:
1. She starts by walking $20\text{km}$ towards the West.
2. Turning left from West means she faces and walks $20\text{km}$ towards the South.
3. Turning left from South means she faces and walks $20\text{km}$ towards the East.
4. Currently, she is facing East. Now, she takes a $45^{\circ }$ turn towards her left.

The direction $45^{\circ }$ to the left (counter-clockwise) of East lies exactly between East and North, which is the North-East direction.