From my house, I walked $30\text{km}$ to the North. Then I turned West and covered $20\text{km}$ and then covered $10\text{km}$ turning South. Finally turning to the East, I covered $20\text{km}$. In which direction am I standing from my house?

Let's track the movement step-by-step on a coordinate plane starting at $(0,0)$:
1. Walked $30\text{km}$ North: New position is $(0,30)$.
2. Turned West and walked $20\text{km}$: New position is $(-20,30)$.
3. Turned South and walked $10\text{km}$: New position is $(-20,30-10)=(-20,20)$.
4. Turned East and walked $20\text{km}$: New position is $(-20+20,20)=(0,20)$.

The final coordinates are $(0,20)$. Since the $x$ -coordinate is $0$ and the $y$ -coordinate is positive, the person is standing exactly to the North of the starting point (house).