Clock

1.

An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? Angle traced by the hour hand in 6 hours = 360 x 6 º = 180º 2.  The reflex angle between the hands of a clock at 10.25 is: Explanation: Angle traced by hour hand in 125 hrs = 360 x 125 º = 312 1 º . 12 12 12 2 Angle traced by minute hand in 25 min = 360 x 25 º = 150º. 60  Reflex angle = 360º - 312 1 - 150 º = 360º - 162 1 º = 197 1 . 2 2 2 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