Correct Option (4)
North–West
Explanation
The house faces East, implying its backside is towards the West. The man's movements can be analyzed as follows:
- Initially, he walks 25 meters down the backside of his house, which means 25 meters towards the West.
- He then turns to his right. From a Westward direction, a right turn leads North. He walks 50 meters North.
- Subsequently, he turns to his left. From a Northward direction, a left turn leads West. He walks another 25 meters West.
To determine his final position relative to the starting point:
- Total displacement in the West direction = 25 meters (initial) + 25 meters (final) = 50 meters West.
- Total displacement in the North direction = 50 meters.
Therefore, his final position is 50 meters West and 50 meters North from the starting point. This composite direction is North–West.
Incorrect Options
Options (1) South–East, (2) South–West, and (3) North–East are incorrect because the sequence of movements does not lead to these directions. The man's path involves initial movement towards the West, followed by North, and then West again. At no point does his displacement include a component towards the South or East relative to his starting position, thus eliminating these options.
