A man went $15\text{km}$ towards North, then turned East and covered $15\text{km}$ and turned to the left. Again after $15\text{km}$ he turned to the right and covered $15\text{km}$ to reach the destination. How far and in which direction is he from his starting point?

Let the starting point be at the origin $O(0,0)$.
1. Moves $15\text{km}$ North $⟹$ position reaches $(0,15)$.
2. Turns East and moves $15\text{km}$ $⟹$ position reaches $(15,15)$.
3. Turns to the left (facing East, turning left means heading North) and covers $15\text{km}$ $⟹$ position reaches $(15,15+15)=(15,30)$.
4. Turns to the right (facing North, turning right means heading East) and covers $15\text{km}$ $⟹$ final destination point $D$ is $(15+15,30)=(30,30)$.

Total displacement along the East axis ($x$ -coordinate) = $30\text{km}$.
Total displacement along the North axis ($y$ -coordinate) = $30\text{km}$.

Shortest distance using Pythagoras theorem:

$$\text{Distance}=\sqrt{30^2+30^2}=\sqrt{900+900}=\sqrt{1800}=30\sqrt{2}\text{km}$$

Since both coordinates are positive, the direction with respect to the starting point $(0,0)$ is North-East.