3.  A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:
Explanation:
Angle traced by hour hand in 12 hrs = 360º.
Angle traced by hour hand in 5 hrs 10 min. i.e.,  31  hrs =   360  x  31   º  = 155º. 
6  12  6 
4.  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 hrs 15 min. =  37  hrs. 
4 
3 min. 5 sec. of this clock = 3 min. of the correct clock.
 37  hrs of this clock =  1  hrs of the correct clock. 
720  20 
 37  hrs of this clock =   1  x  720  x  37   hrs of the correct clock. 
4  20  37  4 
= 9 hrs of the correct clock.
The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.
5.  How much does a watch lose per day, if its hands coincide every 64 minutes?
Explanation:
55 min. spaces are covered in 60 min.
60 min. spaces are covered in   60  x 60  min.  = 65  5  min. 
55  11 
Loss in 64 min. =   65  5   64   =  16  min. 
11  11 
Loss in 24 hrs =   16  x  1  x 24 x 60  min.  =  32  8  min. 
11  64  11 
6.  At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together? Explanation:
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   60  x 5  min  = 5  5  min. 
55  11 
Required time = 5  5  min. past 7. 
11 




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