A left home and cycled $10\text{km}$ towards north, then turned right and cycled $5\text{km}$ and then again turned right and cycled $10\text{km}$. After this he turned left and cycled $10\text{km}$. How many kilometers and in which direction will he have to cycle to reach his home straight?

Let's follow A's coordinates from his starting home position $O(0,0)$:
1. He travels $10\text{km}$ North to $A(0,10)$.
2. He turns right (East) and travels $5\text{km}$ to $B(5,10)$.
3. He turns right (South) and travels $10\text{km}$ to $C(5,0)$.
4. From $C$, facing South, he turns left (East) and travels $10\text{km}$ to reach final point $D(15,0)$.

His final location $D$ is $15\text{km}$ directly East of his home $O(0,0)$. To return straight back to his home from point $D$, he must travel a distance of $15\text{km}$ in the West direction.