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Solutions
At 4 O’ clock, both the hands are 20 minute spaces apart.
Case 1 : Minute hand is 20 minute spaces apart. In this case, the minute hand has to gain (20-3) i.e. 17 minute spaces.
Now, 55 minute are gained in 60 minute.
Hence,17 minute spaces are gained in 
Hence, the hand will be 3 minutes spaces apart at
past 4.
Case 2 : Minute hand is 3 minute spaces ahead of the hour hand.
In this case, the minute hand has to gain (20+3) = 23 minutes spaces
Now, 55 minute are gained in 60 minute.
Hence,23 minute spaces are gained in 
Hence, the hand will be 3 minutes spaces apart at
past 4.