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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