If south-east becomes east and north-west becomes west, and all other directions are changed in the same manner, then what will be the direction for north?

North becomes North-West.

Measure directions clockwise from North as 0 degrees.

South-east at 135 becomes East at 90, a shift of -45 degrees.

North-west at 315 becomes West at 270, again -45 degrees.

Applying -45 to North at 0 gives -45, which is 315.

The 315-degree direction is North-West.