A person whose house faces East, walks 200 m West, then 500 m in South direction, which direction should be take to reach his home?

North-East

Since A person whose house faces East, and he starts moving in the  West direction for 200 meters.

After that, he goes in the South direction for 500 m, which will take him towards the West-South direction.

A person whose house faces East, 

So, for reaching back to the house.

Thus, he needs to go to 538.51 m in the North-East direction for reaching home.