Study the following information carefully and answer the questions below: Eight balls of different colours stuck on a snooker board at different direc...

Study the following information carefully and answer the questions below:
Eight balls of different colours stuck on a snooker board at different directions and at some distance from each other.
The black ball is 50 inches to the west of the green ball. The pink ball is 70 inches to the east of the purple ball. The
grey ball is 20 inches to the north of the magenta ball which is 30 inches to the west of the yellow ball. The black ball
is 40 inches to the south of the purple ball. The green ball is 40 inches to the north of the white ball. The grey ball is
30 inches to the west of the white ball.

Question: In which direction is the black ball located with respect to the magenta ball?