Ajit walks $2\text{km}$ towards East and then he turns South and walks $16\text{km}$. Then he turns East and walks $5\text{km}$. Now, in which direction is he from his starting point?

Let's trace Ajit's movement step-by-step from the starting point $(0,0)$:
1. Starts at $(0,0)$.
2. Walks $2\text{km}$ East $\to$ New coordinate is $(2,0)$.
3. Turns South and walks $16\text{km}$ $\to$ New coordinate is $(2,-16)$.
4. Turns East and walks $5\text{km}$ $\to$ Final coordinate is $(2+5,-16)=(7,-16)$.

The final coordinate $(7,-16)$ has a positive x-coordinate (East) and a negative y-coordinate (South).
Therefore, relative to the starting point $(0,0)$, Ajit is in the South-East direction.