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The minute hand of a clock

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Joined: 20 Oct 2010
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The minute hand of a clock [#permalink] New post 24 Oct 2010, 10:57
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

55% (01:02) correct 45% (00:31) wrong based on 20 sessions
Help me to find out...........
The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day(24Hours) does the clock gain or lose?

1 1440/143 Min
2 720/11 Min
3 5/11 Min
4 340/41 Min
5 511/11 Min
[Reveal] Spoiler: OA

Last edited by sreejas on 24 Oct 2010, 12:24, edited 2 times in total.
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Re: The minute hand of a clock [#permalink] New post 24 Oct 2010, 11:10
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sreejas wrote:
Help me to find out...........
The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day(24Hours) does the clock gain or lose?

1 440/43 Min
2 720/11 Min
3 5/11 Min
4 340/41 Min
5 511/11 Min


In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.
To be together again, the minute hand must gain 60 minutes over the hour
hand.
55 min. are gained in 60 min.
60 min are gained in (60/55) x 60 min =720/11 min.
But, they are together after 65 min.
Gain in 65 min =(720/11)-65 =5/11min.
Gain in 24 hours =(5/11 * (60*24)/65)min =1440/143
The clock gains 1440/143 minutes in 24 hours.


Answer is A.

Consider giving KUDOS if it is helpful to u all.Thanks.

Last edited by ankitranjan on 24 Oct 2010, 12:38, edited 1 time in total.
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Re: The minute hand of a clock [#permalink] New post 24 Oct 2010, 11:30
sreejas wrote:
Help me to find out...........
The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day(24Hours) does the clock gain or lose?

1 440/43 Min
2 720/11 Min
3 5/11 Min
4 340/41 Min
5 511/11 Min


in 12 hours hour clock covers 360 degree => 1 hour = 30 degree => 60 min = 30 degree
=> hour clock covers 1/2 degree in 1 minute.

the minute clock covers 360 degree in 6 minutes => 6 degree in 1 minute

=> relative time between them = 6 -1/2 = 11/2 minute.

Time taken by their relative distance to be zero = 11/2 * 360 degree = 720/11

but it is taking 65 minutes.

thus time gained = 720/11 - 65 = (720-715)/11 = 5/11

But this time is gained in 65 minutes.
Time gained in 24 * 60 minutes = \frac{5}{11} * \frac{1}{65}* 24*60

this is close to 10 minutes. A is also close to 10 minutes. So A?

to be precise:
24*60/65 is 22 + 10/65 => it the clocks will meet 22 times in a day.

=> 5/11 * 22 = 10 minutes till they meet for the last time.i.e. time gained will be slightly greater than 10.

time difference = 24*60 - 22*65 = 10 minutes.

time gained in 65 minutes = 5/11
time gained in 10 minutes = 10/143

hence the answer = 10 + 10/143

the answer is quite near to A.....is there any typo? the answer should be 1440/143
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Re: The minute hand of a clock   [#permalink] 24 Oct 2010, 11:30
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