If 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?

The correct option is North-West.

Let us understand the standard directions first. The four main cardinal directions in clockwise order are North, East, South, and West, each separated by an angle of 90 degrees.
The intermediate (ordinal) directions lie exactly halfway between the cardinal directions, at 45 degrees:
- North-East (NE) lies between North and East.
- South-East (SE) lies between East and South.
- South-West (SW) lies between South and West.
- North-West (NW) lies between West and North.

Now, let us analyze the changes described in the question:
1. We are told that "If becomes east" (which refers to the original North direction based on standard direction puzzles of this type, or we can look at the second clue to find the rotation rule).
2. Let's look at the second change: "North-West becomes West".
In standard directions, West is 45 degrees counter-clockwise from North-West. Therefore, the direction North-West has rotated 45 degrees counter-clockwise to become West.
This means the entire direction compass is rotated by 45 degrees in a counter-clockwise direction.

Applying this same counter-clockwise rotation of 45 degrees to find what North becomes:
If we look at the standard compass, the direction that is 45 degrees counter-clockwise from North is North-West.
Therefore, under this rotation, the direction for North will become North-West.