How often between 11 O'clock and 12 O'clock a | vedclass

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(B) In a clock,there are $60$ minute spaces in one full rotation ($60$ minutes). At $11$ $O$'clock,the minute hand is at the $12$ position ($0$ minute

Vedclass · Accepted Answer

$56$

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(B) In a clock,there are $60$ minute spaces in one full rotation ($60$ minutes). At $11$ $O$'clock,the minute hand is at the $12$ position ($0$ minute mark) and the hour hand is at the $11$ position ($55$ minute mark). The distance between them is $5$ minute spaces. As the minute hand moves from the $0$ minute mark to the $60$ minute mark,it passes through every minute position. Since the hour hand also moves slightly,the relative distance between the hands changes continuously. However,the question asks for the number of times the hands are an integral number of minutes apart between $11:00$ and $12:00$. There are $60$ total minute positions. Excluding the starting position at $11:00$ (where they are $5$ minutes apart) and considering the movement until $12:00$,the hands will be at an integral minute distance $56$ times.

How often between $11$ $O$'clock and $12$ $O$'clock are the hands of a clock in integral number of $minutes$ apart (in $times$)?

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