Clock - General Questions

Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.

The watch gains		2 + 4	4	min.	or	34	min. in 170 hrs.
			5			5

2 min. are gained in		170 x	5	x 2	hrs	= 50 hrs.
			34

 Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e., it will be correct at 2 p.m. on Wednesday.

In 12 hours, the hands coincide or are in opposite direction 22 times.

 In 24 hours, the hands coincide or are in opposite direction 44 times a day.

At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.

To be coincident, it must gain 15 min. spaces.

55 min. are gained in 60 min.

15 min. are gained in		60	x 15	min	=	16	4	min.
		55					11

The hands are coincident at 16	4	min. past 3.
	11

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

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.

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°.