Question

At what time between 4 and 5 are the hands 2 minute spaces apart?

Answer 1

At 4 o'clock the two hands are 20 minute spaces apart
Case I : When minute hand is 2 minute spaces behind hour hand
In this case the minute hand will have to gain (20 - 2) i.e. 18 minute spaces
Now 18 minute spaces will be gained in
6055×18=21611=197116055×18=21611=19711 min
Hence they will be 2 minute part at 1971119711 min past 4
Case II : When minute hand is 2 minute spaces ahead of the hour hand
In this case minute-hand will have to gain (20 + 2) i.e. 22 minute spaces
Now 22 minute spaces will be gained in 6055×22=246055×22=24 min
Hence the habds will be 2 minute apart at 24 minute past 4.