A man starts walking in the north-easterly direction from a particular point. After walking a distance of 500 metres, he turns southward and walks a distance of 400 metres. At the end of this walk he is situated

This problem can be solved using the properties of a right angled triangle.

The man starts at the origin. Walking 500 metres in a north easterly direction represents the hypotenuse of a right angled triangle. When he turns south and walks 400 metres, this distance represents one side of the triangle specifically the vertical displacement.

To find his final position relative to the starting point, we use the Pythagorean theorem: base squared plus height squared equals hypotenuse squared.

Let the horizontal distance from the start be X. X squared plus 400 squared equals 500 squared. X squared plus 160000 equals 250000. X squared equals 90000. X equals 300.

Because the north easterly path and the southward turn form a right angle with the horizontal line extending from the starting point, he ends up exactly 300 metres east of his original position. The vertical climb of the north east walk is cancelled out by the 400 metre walk south, leaving him on the same horizontal axis as the starting point.

Therefore, the correct option is C.