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Angle traced by hour hand in 125/12 hrs =
Angle traced by minute hand in 25 min =
∴ Reflex angle = 360^{0} 
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.
A clock is started at noom. By 10 mimutes past 5, the hour hand has turned through:
Angle traced by hour hand in 12 hrs = 360º.
Angle traced by hour hand in 5 hrs 10 min. i.e., 31/6 hrs
= (360/12)*(31/6)°
= 155º
A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:
Time from 7 a.m. to 4.15 p.m. = 9 hours 15 min = 37/4 hours
3 min 5 sec of this clock = 3 min. of the correct clock.
⇒ 37/720 hours of this clock = 1/20 hours of the correct clock
⇒ 37 hours of this clock = (1/20 x 720/37 x 37/4) hours of the correct clock.
= 9 hours of the correct clock.
∴ The correct time is 9 hours after 7 a.m. i.e., 4 p.m
At what time between 5.30 and 6 will the hands of a clock be at right angles?
At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.
55 min. spaces are gained in 60 min.
40 min. spaces are gained in
∴ Required time = min. past 5.
A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?
Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.
∴ The watch gains in 170 hrs.
Now, 34/5 min. are gained in 170 hrs.
∴ 2 min. are gained in
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.
At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?
When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock, they are 25 min. spaces apart.
Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.
5 min. spaces are gained in
∴ Required time = min. past 7.
At what angle the hands of a clock are inclined at 15 minutes past 5?
15 past 5 means quarter past 5 = (5:15)
⇒ (11*15  60*5)/2 = 67.5
A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?
Time from Monday noon (12 o' clock) to following Monday 2 pm = 7 day 2 hours
= 7×24+2
= 168+2
= 170 hours
Total time gained Monday noon (12 o' clock) to following Monday 2 pm = 2 min + 4 min 48 sec
The given watch gains 34/5 mins in 170 hours
Given that the said watch was 2 minutes low at Monday noon. Hence when it gained 2 minutes, the time was correct.
The given watch gains 34/5 mins in 170 hours
⇒ The given watch gains 2 mins in
= 5 * 5 * 2 hours = 50 hours
Hence the time was correct after 50 hours from Monday noon = after 2 days 2 hours from Monday noon = 2 pm on Wednesday
The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
The angle between hour and minute hand in 4:20 is 10 degrees.
For a minute, the hour hand rotates by 30/60 = 1/2 degrees.
hence, for 20 minutes it rotates by an angle of 20*1/2 = 10 degrees.
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