The minute hand of a clock overtakes the hour hand at intervals of 65

Question

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?

A. 1440/143 Min
B. 720/11 Min
C. 5/11 Min
D. 340/41 Min
E. 511/11 Min

ankitranjan · Accepted Answer

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.
 
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gurpreetsingh · Answer

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

NanditaParmar · Answer

Answer - For a normal clock, time taken by minute hand to overtake the hour hand = 65 + 5/11 minutes. 
Since for this clock, the minute hand takes only 65 minutes, the clock gains 5/11 minutes every 65 minutes. 
Therefore, in 24 hours, the clock gains 1440/143 minutes.

The minute hand of a clock overtakes the hour hand at intervals of 65

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The minute hand of a clock overtakes the hour hand at intervals of 65

Prep Toolkit

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