To answer the questions on this topic, always draw a rough diagram representing directions East, West, North, South, North-West, North-East, South-West, South-East.
Now draw the diagram, as per the given instructions.
As per the given directions, Aman runs 10 m north, turns left and runs another 20 m.
Then, he turns right, walks another 10 m, again turns right and walks another 50 m.
So, he is in North-East direction with respect to his initial position.