At what time between 5 and 6 o'clock are the hands of a clock 3minapart?

   

At 5 o'clock, the minute hand is 25 min. spaces 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 spaces. 55 min. are gained in 60 min.

22 min. are gained in (60*22)/55min. = 24 min.

:. The hands will be 3 min. apart at 24 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 x 28_)/55=346/11

The hands will be 3 min. apart at 346/11 min. past 5.