Arjun is facing south, then he turns 45
∘
right and goes 50 m, then turns north-west to move 50 m and from there 50 m to west. In which direction/place is he from his original place?

Let's trace Arjun's path step-by-step from his initial starting point O(0,0):
Initial Facing Direction: South.

First Turn & Move: He turns 45
∘
to his right, which means he is now facing the South-West direction. He walks 50 m in this direction to reach a point A.

Second Turn & Move: From point A, he turns towards the North-West direction and moves 50 m to reach point B. Since the path OA (South-West) and AB (North-West) are perpendicular (90
∘
apart) and of equal lengths (50 m), they form a right-angled isosceles triangle with the line along the horizontal west axis. Thus, point B lies exactly due West of the starting point O.

Third Move: From point B, he walks 50 m further due West to reach point C.

Since point B is to the west of O, moving further west to point C keeps him directly to the West of his original starting point.