Through how many degrees does hour hand in a clock move as the time changes from 3 hours 12 minutes to hours ?

The question text is truncated. The end time is almost certainly 6 o'clock, since 84 only works if the hour hand runs from 3:12 to 6:00. I'm working on that assumption.

The hour hand moves 30 degrees per hour, or 0.5 degrees per minute. From 3:12 to 6:00 is 2 hours 48 minutes, which is 2.8 hours. So 2.8 x 30 = 84 degrees, which is option D.

Quick check using positions: at 3:12 the hour hand is at 90 + 6 = 96 degrees from 12. At 6:00 it is at 180 degrees. The difference is 84 degrees.

• A) 105 is wrong. It corresponds to a span of 3.5 hours, which doesn't match the 2h48m interval.
• B) 99 is wrong. It corresponds to 3.3 hours, or 3 hours 18 minutes, which is not the interval here.
• C) 90 is wrong. It is the movement from 3:00 to 6:00, which ignores the 12 minutes already elapsed.

The concept is angular speed of clock hands, a basic arithmetic topic that comes up often in Prelims. It is a routine question, but speed is what you need to finish the paper.

Trap: Aspirants compute the hour hand's movement as whole hours only and forget the 0.5 degrees per minute contribution, which lands them on 90.