Between 12 noon and 2:30 in the afternoon of the same day, through how many degrees does the hour hand of a clock move?

Introduction / Context:
This question checks your understanding of how the hour hand of an analog clock moves and how to convert time intervals into angular movement in degrees. It is a simple but important concept that often appears in aptitude tests under the topic of clocks and time.

Given Data / Assumptions:

- Start time = 12:00 noon.
- End time = 2:30 pm on the same day.
- The hour hand completes one full circle, which is 360 degrees, in 12 hours.
- The hour hand moves at a constant rate.

Concept / Approach:
The hour hand moves 360 degrees in 12 hours. Therefore, its angular speed is 360 / 12 degrees per hour. Once we know this rate, we find the total elapsed time between 12:00 and 2:30, convert that to hours, and multiply by the angular speed. This directly gives the number of degrees through which the hour hand has moved.

Step-by-Step Solution:
Time interval from 12:00 to 2:30 = 2 hours 30 minutes. Convert 2 hours 30 minutes to hours: 2.5 hours. Hour hand speed = 360 degrees in 12 hours. So angular speed = 360 / 12 = 30 degrees per hour. Total angle turned = angular speed * time. Total angle = 30 * 2.5 = 75 degrees.

Verification / Alternative check:
We can also reason by half hours. In one hour, the hour hand moves 30 degrees. In half an hour, it moves 15 degrees. From 12:00 to 2:00 pm is 2 hours, so the hour hand moves 2 * 30 = 60 degrees. From 2:00 to 2:30 pm is another 15 degrees. Total = 60 + 15 = 75 degrees, which matches the earlier calculation.

Why Other Options Are Wrong:
720°: This is the angle for two full rotations of the clock, which would take 24 hours, not 2.5 hours.
180°: This corresponds to 6 hours of movement (half a day on the clock), not 2.5 hours.
65°: This does not correspond to any simple multiple of the per hour movement of the hour hand and does not match the correct calculation.

Common Pitfalls:
A frequent mistake is to confuse the movements of the hour hand and the minute hand. Another error is to forget to convert 30 minutes into 0.5 hours and instead treat it as 30 hours or ignore it entirely. Always convert the entire time interval into hours before multiplying by the hourly angular speed.

Final Answer:
Between noon and 2:30 pm, the hour hand moves through 75°.