Explanation:

To determine Rohan's final direction, we need to calculate the total angular displacement from his starting position. **Step 1: Identify the starting direction.** * Rohan is initially facing West. **Step 2: Calculate the total clockwise turn.** * First turn: $45^{\circ}$ clockwise. * Second turn: $180^{\circ}$ clockwise. * Third turn: $270^{\circ}$ clockwise. * Total clockwise turn = $45^{\circ} + 180^{\circ} + 270^{\circ} = 495^{\circ}$. **Step 3: Simplify the total turn by accounting for full rotations.** * A full circle is $360^{\circ}$. Any turn greater than $360^{\circ}$ can be simplified by subtracting multiples of $360^{\circ}$. * $495^{\circ} = 360^{\circ} + 135^{\circ}$. * This means Rohan effectively turns $135^{\circ}$ clockwise from his initial direction (West). **Step 4: Determine the final direction.** * Starting from West, a $90^{\circ}$ clockwise turn leads to North. * A $135^{\circ}$ clockwise turn from West means turning $90^{\circ}$ to North and then an additional $135^{\circ} - 90^{\circ} = 45^{\circ}$ clockwise from North. * $45^{\circ}$ clockwise from North is North-East. \nAlternatively, using degrees relative to North (where North is $0^{\circ}$ or $360^{\circ}$, East is $90^{\circ}$, South is $180^{\circ}$, West is $270^{\circ}$): * Starting direction: West, which is $270^{\circ}$. * Add the effective clockwise turn: $270^{\circ} + 135^{\circ} = 405^{\circ}$. * Since $405^{\circ}$ is greater than $360^{\circ}$, subtract $360^{\circ}$ to find the equivalent angle within a single rotation: $405^{\circ} - 360^{\circ} = 45^{\circ}$. * The direction corresponding to $45^{\circ}$ clockwise from North is North-East. \nTherefore, Rohan is now facing North-East. * **Option 1 (North East):** This is the correct final direction after a $135^{\circ}$ clockwise turn from West. So, this is the correct answer. * **Option 2 (North West):** This would be $45^{\circ}$ counter-clockwise from North, or $315^{\circ}$ clockwise from North. This is incorrect. * **Option 3 (South East):** This would be $135^{\circ}$ clockwise from North. This is incorrect as Rohan started from West. * **Option 4 (South West):** This would be $225^{\circ}$ clockwise from North. This is incorrect.