Rahul placed his wristwatch flat on a table in such a way that at 6:00 P.M. the hour hand points exactly towards the North. Keeping the watch fixed in that position, in which direction will the minute hand be pointing at 9:15 P.M.?

Introduction:
This direction–sense problem uses a clock face as a reference for directions. Rahul rotates the clock so that at a specific time (6:00 P.M.) the hour hand points to a given cardinal direction (North). The orientation of the entire dial is thus fixed. We are then asked to find the direction of the minute hand at another time (9:15 P.M.) with respect to the same orientation.

Given Data / Assumptions:
• At 6:00 P.M., the hour hand points to North.• The watch lies flat and stays fixed on the table after it is placed.• The question asks for the direction of the minute hand at 9:15 P.M., measured against the same compass directions.• We use the standard positions: on a normal clock face, 12 is at the top, 3 at the right, 6 at the bottom, and 9 at the left.

Concept / Approach:
At 6:00 P.M., the hour hand normally points at the 6 on the dial, which is downward relative to 12. Rahul rotates the entire clock so that this downward direction (towards 6) now points North. That rotation also fixes new compass directions for 12, 3, and 9. After that, we simply determine where the minute hand points at 9:15 P.M. on the dial and translate that into the corresponding compass direction.

Step-by-Step Solution:
Step 1: At 6:00 P.M., in a standard orientation, the hour hand points to the 6, which is vertically down from the centre.Step 2: Rahul places the watch so that this downward direction now points to the North. Therefore, the 6-mark direction corresponds to North.Step 3: Since 12 is opposite 6, the 12-mark direction now corresponds to South.Step 4: On the usual clock, 3 lies to the right and 9 to the left of 12. With 12 now pointing South, 3 points West and 9 points East (because the entire dial has been rotated 180 degrees compared with the normal North-at-12 assumption).Step 5: At 9:15 P.M., the minute hand points exactly at the 3 on the dial (because it is 15 minutes past the hour).Step 6: As established, the 3-mark direction in this orientation points towards the West.Step 7: Therefore, at 9:15 P.M., Rahuls minute hand points West.

Verification / Alternative check:
We can verify by imagining the dial: if the hour hand at 6 points North, then the dial is effectively upside down compared to the usual North-at-12 orientation. That makes 3 become West and 9 become East. The minute hand at 15 minutes always aims at 3, independent of the hour hand. Hence, West is consistent and there is no ambiguity in the direction.

Why Other Options Are Wrong:
South and North refer to directions associated with the 12 and 6 marks under this rotated arrangement, not with the 3 mark. South-East and North-West would require intermediate diagonal positions that the minute hand does not occupy at exactly 9:15 P.M. Therefore, they cannot be correct. West is the only direction that matches the 3-mark in the rotated dial.

Common Pitfalls:
A frequent mistake is to assume 12 always points North and then work from that, forgetting that the entire clock has been rotated. Others confuse the hour hand's position at 9:15 P.M. with the minute hand's position, even though the question asks only about the minute hand. Keeping the dial orientation fixed after the initial rotation and focusing on the correct hand avoids such errors.

Final Answer:
With the clock oriented so that the 6-mark points North, the minute hand at 9:15 P.M. points towards the West.