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Quiz: Clocks

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Number of Questions: 20

Question: 6 -

Find the number of times the hour hand and the minute hand of a clock are at right angle in a day.

Options:

  1. 44

  2. 24

  3. 42

  4. 48

    5. Answer:

    44
    Solution:

    In 12 hours, the hands of a clock are at right angle 22 times.
    Hence in a day they are at right angle 44 times.

Question: 7 -

The reflex angle between the hands of a clock at 9.35 is:

Options:

  1. 300°

  2. 282.5°

  3. 77.5°

  4. 270°

    5. Answer:

    282.5°
    Solution:

    Angle traced by the hour hand in 12 hours = 360°
    Angle traced by the hour hand in 9 hours 35 minutes = (360 * 115) / (12 * 12) = 287.5°
    Angle traced by the minute hand in 60 minutes = 360°
    Angle traced by the minute hand in 35 minutes = 210°
    Therefore, the angle between the hour hand and the minute hand at 9.35
    = (287.5 – 210) = 77.5°
    Reflex angle = 360 – 77.5 = 282.5°

Question: 8 -

Find the angle between the hour hand and the minute hand of a clock when the time is 5.45.

Options:

  1. 95°

  2. 100°

  3. 97.5°

  4. 90°

    5. Answer:

    97.5°
    Solution:

    Angle traced by the hour hand in 12 hours = 360°
    Angle traced by the hour hand in 5 hours 45 minutes = (360 * 23) / (12 *4) = 172.5°
    Angle traced by the minute hand in 60 minutes = 360°
    Angle traced by the minute hand in 45 minutes = 270°
    Therefore, the angle between the hour hand and the minute hand at 5.45
    = (270 – 172.5) = 97.5°

Question: 9 -

A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?

Options:

  1. 45 min. past 12.

  2. 48 min. past 12. 

  3. 46 min. past 12. 

  4. 47 min. past 12. 

    5. Answer:

    48 min. past 12. 
    Solution:

    Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours. 

    24 hours 10 min. of this clock = 24 hours of the correct clock. 

    145/6

     hrs of this clock = 24 hours of the correct clock. 

    29 hours of this clock = 24*(6/145)*29

     hrs of the correct clock 

    = 28 hrs 48 min of the correct clock. 

    Therefore, the correct time is 28 hrs 48 min. after 8 a.m. 

    This is 48 min. past 12.

Question: 10 -

A clock was set right at 2 p.m. It gains 5 seconds in 3 minutes, and it indicates 8.30 a.m. the next morning, then the true time is:

Options:

  1. 8.00 a.m.

  2. 7.30 a.m.

  3. 7.45 a.m.

  4. 8.30 a.m.

    5. Answer:

    8.00 a.m.
    Solution:

    Time elapsed from 2 p.m. to 8.30 a.m. = 18 hours 30 minutes = 1110 minutes.
    Now, 3 minutes and 5 seconds of the given clock is 3 minutes of the correct clock.
    Therefore, 1110 minutes of this clock is (1110 * 3) / (37/12) minutes of the correct clock.
    = 1080 minutes = 18 hours of the correct clock
    Hence, the correct time is 8 a.m.