Understanding Direction and Movement Puzzles

This question requires us to trace Mukesh's path and determine his final position relative to his starting point. We need to carefully follow the sequence of movements and turns described.

Analyzing Mukesh's Movement Steps

Let's break down the steps Mukesh takes:

• Starting Point and Initial Direction: Mukesh starts at a specific point, let's call it the origin. He is initially facing South.
• First Movement: He walks 5 km straight from his starting position. Since he was facing South, he moves 5 km in the South direction from the origin. Let's assume the origin is (0,0). His position after the first movement is (0, -5) if we consider South as negative on the y-axis.
• Second Movement: From his current position (5 km South of origin), he turns 90° to his right. If you are facing South, turning 90° right means you turn towards the West. He then walks 5 km in this new direction (West). So, from (0, -5), he moves 5 km West. His new position is (-5, -5) assuming West is negative on the x-axis.
• Third Movement: From his current position (-5, -5) and facing West, he turns at a 45° angle to his left. If you are facing West, a 45° turn to the left puts you in the South-West direction. He walks 3 km in this South-West direction. This movement is in a direction that is between South and West relative to his current position.

Determining the Final Position Relative to the Start

Let's visualize the overall path:

1. He moved directly South from the start.
2. He moved directly West from that South point.
3. He moved South-West from that point.

All his movements have taken him away from the origin in directions that are either South, West, or South-West. If you start at the origin (0,0) and move first into the South-West quadrant (by moving South and West), any subsequent movement further into the South-West direction will keep you within or further into the South-West quadrant relative to the origin.

Since all segments of his journey (South, then West, then South-West) are predominantly in the lower-left region relative to his starting point, his final position will be in the South-West direction from where he began.

The cumulative effect of these movements is a displacement primarily in the South and West directions from the starting point. Therefore, his final location is in the South-west direction relative to his actual starting position.

Revision Table: Key Direction Concepts

Additional Information on Direction Puzzles

Direction and distance puzzles are common in reasoning tests. To solve them effectively:

• Draw a diagram: Sketching the path helps visualize the movements and final position.
• Use a coordinate system: Assigning coordinates (x,y) can help track the exact position, especially for complex paths or when calculating final distance. However, for determining direction, sometimes a simple diagram is enough.
• Break down complex turns: Understand that turns are relative to the current direction. A 45° turn left from West is different from a 45° turn left from South.
• Focus on the final position relative to the start: The question asks where he is from his *actual position* (starting point).

In this specific problem, the movements are 5km South, then 5km West, then 3km South-West. All these displacements contribute towards moving away from the origin into the South-West region of a coordinate plane. Therefore, the final direction from the start is South-west.