At 4 o'clock, the hands of the watch are 20 min. spaces apart.

To be in opposite directions, they must be 30 min. spaces apart.

Minute hand will have to gain 50 min. spaces.

55 min. spaces are gained in 60 min.

50 min. spaces are gained in		60	x 50	min. or 54	6	min.
		55			11

Required time = 54	6	min. past 4.
	11

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).

So, in a day, the hands point in the opposite directions 22 times.

To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.

55 min. spaces gained in 60 min.

45 min. spaces are gained in		60	x 45	min or 49	1	min.
		55			11

The hands are together at 49	1	min. past 9.
	11

Angle traced by hour hand in	17	hrs =		360	x	17		�	= 255.
	2			12		2

Angle traced by min. hand in 30 min. =		360	x 30		�	= 180.
		60

Required angle = (255 - 180)� = 75�.

In 12 hours, they are at right angles 22 times.

In 24 hours, they are at right angles 44 times.