Question:At what time between 5 and 6 o'clock are the hands of a 3 minute apart ?
Answer At 5 o'clock, the minute hand is 25 min. space behind the hour hand. Case I: Minute hand is 3 min.spaces behind the hour hand. In this case, the minute hand has to gain (25 - 3) = 22 minute space 55 min are gained in 60 min. 22 min. are gained in` (60/55 xx 22)` min. = 24 min :. The hands will be 3 min. apart at` 31 5/11` min. past 5. Case II : Minute hand is 3 min.spaces ahead of the hour hand. In this case, the minute hand has to gain (25 + 3) = 28 minute spaces. 55 min.are gained in 60 min. 28 min. are gained in` (60/55 xx 28)` `= 31 5/11` min. :. The hands will be 3 min. apart at `31 5/11` min. past 5.
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At what time between 5 and 6 o'clock are the hands of a 3 minute apart ?