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# Clock

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VP
Joined: 18 May 2008
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Clock [#permalink]  16 Nov 2008, 22:15
00:00

Difficulty:

5% (low)

Question Stats:

66% (02:22) correct 33% (00:09) wrong based on 3 sessions
What is the angle between the minute and the hour hand of the clock which shows 12:24?

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Director
Joined: 14 Aug 2007
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Re: Clock [#permalink]  16 Nov 2008, 22:45
ritula wrote:
What is the angle between the minute and the hour hand of the clock which shows 12:24?

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At 12:24
-minute hand will be at 24*6 = 144 degrees from position of 12.
- Hour hand will move by 2*6 = 12 degree during the same time

So the difference between the two hands will be 144-12 = 132 degrees.
Manager
Joined: 14 Oct 2008
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Re: Clock [#permalink]  17 Nov 2008, 04:06
1
KUDOS
hour hand moves 5 minutes when minute hand moves 60 minutes. Hence when minute hand moved 24 minutes, hour hand moved 24 *5 / 60 i.e. 2 minutes.
Director
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Re: Clock [#permalink]  17 Nov 2008, 05:19
ritula wrote:
can u pls explain this?
alpha_plus_gamma wrote:

At 12:24
-minute hand will be at 24*6 = 144 degrees from position of 12.
- Hour hand will move by 2*6 = 12 degree during the same time

So the difference between the two hands will be 144-12 = 132 degrees.

yeah, exactly in the way provided by gameCode

gameCode wrote:
hour hand moves 5 minutes when minute hand moves 60 minutes. Hence when minute hand moved 24 minutes, hour hand moved 24 *5 / 60 i.e. 2 minutes.
Manager
Joined: 02 Oct 2009
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Re: Clock [#permalink]  14 Dec 2009, 01:58
I read somewhere there is a direct formula to solve this question..2)
Angle between m and h hand is ( 11/2) *m – 30 * h
can this be apply here? if yes should i take the value of h =12 ..taking this I am not getting the answer..
Math Expert
Joined: 02 Sep 2009
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Re: Clock [#permalink]  14 Dec 2009, 15:19
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Expert's post
KocharRohit wrote:
I read somewhere there is a direct formula to solve this question..2)
Angle between m and h hand is ( 11/2) *m – 30 * h
can this be apply here? if yes should i take the value of h =12 ..taking this I am not getting the answer..

You just should substitute h=0 in it, not h=12.

General formula is:

|\frac{11}{2}m - 30h|

If the result is greater than 180 degrees, subtract it from 360 to get the included angle.

The above can be derived from the fact that:
In 1 minute:
Hour hand moves 0.5 degrees,
Minute hand moves 6 degrees.

AND

In an hour:
Hour hand moves 30 degrees,
Minute hand moves 360 degrees.

Hope it's clear.
_________________
Re: Clock   [#permalink] 14 Dec 2009, 15:19
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