Prem starts from his house and walks 400 metres towards the north. Then he turns left and walks 100 metres. Next he turns left again and walks 200 metres. Finally he turns left once more and walks 100 metres. After completing this path, how far is he from his house?

Introduction / Context:
This problem describes a path taken by Prem with several left turns and asks for his final distance from his starting point, his house. The motion forms a simple shape that can be represented on a coordinate plane. It tests basic understanding of direction changes, along with the idea that some movements may partially cancel out when they occur in opposite directions.

Given Data / Assumptions:

• Prem starts from his house at an origin point.
• He walks 400 m north.
• He turns left from facing north and walks 100 m west.
• He again turns left from facing west and walks 200 m south.
• He turns left once more from facing south and walks 100 m east.
• We only need the straight line distance from his final position back to his house.

Concept / Approach:
We use a coordinate grid for clarity. Let the house be at (0, 0). Movements north increase the y coordinate, movements south decrease it, movements east increase the x coordinate, and movements west decrease it. After tracking all movements, we examine the final coordinates and compute displacement using the distance formula if needed. In this particular case, all horizontal movements cancel exactly, making the calculation especially simple.

Step-by-Step Solution:
Set the starting point at (0, 0). Walk 400 m north to reach (0, 400). Facing north, a left turn leads west, so walk 100 m west to reach (-100, 400). Facing west, a left turn leads south, so walk 200 m south to reach (-100, 200). Facing south, a left turn leads east, so walk 100 m east to reach (0, 200). Final coordinates are (0, 200). Distance from the house is sqrt(0^2 + 200^2) = 200 m.

Verification / Alternative check:
Horizontally, Prem goes 100 m west and then 100 m east, which cancel. Vertically, he first goes 400 m north and then 200 m south, leaving a net 200 m north. Since he is directly north of his house with no east west separation, his straight line distance from home is simply 200 m.

Why Other Options Are Wrong:
Option A: 100 m only accounts for part of the net vertical displacement.
Option B: 300 m exaggerates the remaining northward distance.
Option D: 250 m is not supported by the component calculations.
Option E: None of these is wrong because 200 m is present as a correct choice.

Common Pitfalls:
Students sometimes treat the entire path length as the displacement or forget that the last two horizontal legs cancel. Another pitfall is misinterpreting repeated left turns and drawing the path incorrectly. Keeping a clear sketch or systematic x y record prevents these errors.

Final Answer:
Prem is 200 m away from his house after the described movements.