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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