In a compass every direction is rotated to $135$ degrees from the original direction. In which direction will South-West be if the rotation took towards clockwise direction?

The question asks where the original direction 'South-West' points after the compass itself is rotated clockwise by $135^{\circ }$.
When a compass scale is rotated clockwise by $135^{\circ }$, any fixed direction pointer on the card moves clockwise by $135^{\circ }$.

* South-West is at an angle of $225^{\circ }$ measured clockwise from North.
* Rotating it clockwise by $135^{\circ }$: $225^{\circ }+135^{\circ }=360^{\circ }$ (which is North).
Alternatively, looking at the standard directions:
* Moving $45^{\circ }$ clockwise from South-West leads to West.
* Moving another $90^{\circ }$ clockwise from West leads to North.
* Total clockwise movement = $45^{\circ }+90^{\circ }=135^{\circ }$.
Thus, the position originally corresponding to South-West now points to North.