Question

A man facing west turns 180 degrees clockwise and then he turns 225 degrees anticlockwise . Which direction is he facing now?

• A. North-East
• B. North-West
• C. South-East
• D. South-West

Hint:

Instead of drawing multiple compasses, simply calculate the net angle:
\(225^{\circ} \text{ anticlockwise} - 180^{\circ} \text{ clockwise} = 45^{\circ} \text{ anticlockwise}\).
A \(45^{\circ}\) anticlockwise turn from West points directly to South-West.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
This is a logical reasoning problem involving direction sense and angular rotations.

Step 2: Key Formulas and approach:
Let clockwise turns be represented by positive angles (\(+\)) and anticlockwise turns by negative angles (\(-\)).
Calculate the net angle of rotation from the starting direction of West:
\[ \text{Net Rotation} = \text{Clockwise Rotation} - \text{Anticlockwise Rotation} \] Use the standard direction compass (North, South, East, West) to find the final direction.

Step 3: Detailed Explanation:

• The man is initially facing West.

• First rotation: \(180^{\circ}\) clockwise.

• Second rotation: \(225^{\circ}\) anticlockwise.

• Compute the net rotation:
\[ \text{Net Rotation} = +180^{\circ} - 225^{\circ} = -45^{\circ} \]

• A negative sign indicates that the net rotation is \(45^{\circ}\) in the anticlockwise direction.

• Now, start from West on the compass and rotate \(45^{\circ}\) anticlockwise (which is a turn towards the left, shifting towards South).

• The direction located \(45^{\circ}\) south of West is South-West.


Step 4: Final Answer:
The man is facing South-West now, which corresponds to Option (D).