Problem Solving

What is the angle between the minute and the hour hand of the clock which shows 12:24?



115


120


124


130


132

[email protected] wrote:What is the angle between the minute and the hour hand of the clock which shows 12:24?



115


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132

Minute hand moves by 6° in a minute, whereas hour hand moves ½° in a minute. Hence at 12:24, minute hand will be at 24th minute mark of the clock, and in those 24 minutes the hour hand would have moved by 12° (at the 2 minute mark of the clock) towards the minute hand. Hence, now there are exactly 24 - 2 = 22 minute divisions between the two hands, which include 22 × 6° = [spoiler]132°.

Choose E[/spoiler]

[spoiler]Diagram Attached for help![/spoiler]

[email protected] wrote:What is the angle between the minute and the hour hand of the clock which shows 12:24?



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132

Let's say that at 12:00 the hour hand and the minute hand are both at 0º.
We need to determine the position of each hand after the passing of 24 minutes.

Hour hand:
Every 12 hours, the hour hand travels clockwise all the way around the clock (360º).
Thus, every hour, the distance traveled by the hour hand = (1/12)(360) = 30º.
In 24 minutes -- 2/5 of an hour -- the hour hand travels clockwise 2/5 of its hourly distance:
(2/5)(30) = 12º.

Minute hand:
Every hour, the minute hand travels clockwise all the way around the clock (360º).
Thus, in 24 minutes -- 2/5 of an hour -- the minute hand travels clockwise 2/5 of its hourly distance:
(2/5)(360) = 144º.

Since the minute hand travels clockwise 144º, while the hour hand travels clockwise 12º, the angle between the minute hand and the hour hand = 144-12 = 132º.

The correct answer is E.

Min hand moves an angle of 6 dgrees in 1 min
Hour hand moves an angle of 1/2 degree in 1 min

Relative angular difference between the two hands of clock in a min = 6-(1/2) = 5.5 degrees

in 1 min the angular difference = 5.5 degrees
in 24 mins the angular difference = 5.5 x 24 degrees = 132 degrees ANSWER