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Clock Reasoning

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  1. Question 1 of 24
    1. Question

    In 16 minutes, the minute hand gains over the hour hand by

    Hint

    In 1 hour, the minute hand gains 330° over the hour hand. i.e. in 60 minute, the minute hand gains 330° over the hour hand.
    ∴ In 16 minutes, the minute hand gains over the hour hand by clock-calendar-15018.png

  2. Question 2 of 24
    2. Question

    If the two hands in a clock are 3 minutes divisions apart, then the angle between them is

    Hint

    In a clock, each minute makes 6°
    ∴ 3 minutes will make 6 × 3 = 18°

  3. Question 3 of 24
    3. Question

    What will be the acute angle between hands of a clock at 2 : 30?

    Hint

    At 2’O Clock, Minute Hand will be 10 × 6 = 60° behind the Hour Hand.
    In 30 minutes, Minute Hand will gain 5 ½° × 30 = 150 + 15 = 165°
    ∴Angle between Hour Hand and Minute Hand = 165 – 60 = 105°

  4. Question 4 of 24
    4. Question

    What is the angle between the 2 hands of the clock at 8:24 pm?

    Hint

    Required angle = 240 – 24 × (11/2) = 240 –132 = 108°.

  5. Question 5 of 24
    5. Question

    At what angle the hands of a clock are inclined at 15 minutes past 5 ?

    Hint

    At 15 minutes past 5, the minute hand is at 3 and hour hand slightly advanced from 5. Angle between their 3rd and 5th position.
    Angle through which hour hand shifts in 15 minutes isclock-calendar-15586.png
    ∴Required angle = clock-calendar-15580.png

  6. Question 6 of 24
    6. Question

    Find the angle between the hour hand and the minute hand of a clock when the time is 3.25.

    Hint

    Angle traced by the hour hand in 12 hours = 360°
    Angle traced by it in 3 hrs 25 min. i.e. clock-calendar-15618.png clock-calendar-15612.png
    Angle traced by it in 25 min. clock-calendar-15606.png
    Required angle clock-calendar-15600.png

  7. Question 7 of 24
    7. Question

    If a clock strikes 12 in 33 seconds, it will strike 6 in how many seconds?

    Hint

    In order to strike 12, there are 11 intervals of equal time
    clock-calendar-14218.png
    Therefore, to strike 6 it has 5 equal intervals, it requires 5 × 3 = 15 sec.

  8. Question 8 of 24
    8. Question

    At what time between 7 and 8 o’clock will the hands of a clock be in the same straight line but, not together?

    Hint

    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 in. spaces.
    55 min. spaces are gained in 60 min.
    5 min. spaecs are gained in clock-calendar-14962.png
    clock-calendar-14956.png

  9. Question 9 of 24
    9. Question

    At what approximate time between 4 and 5 am will the hands of a clock be at right angle?

    Hint

    Here H × 30 = 4 × 30 = 120°.
    (Since initially the hour hand is at 4.∴ H = 4).
    Required angle A = 90° and since, H × 30 > A° so, there will be two timings.
    Required time T = ²⁄₁₁ (H × 30 ± A) minutes past H.
    ∴ One timing = ²⁄₁₁ (4 × 30 + 90) minutes past 4.
    = 38 ²⁄₁₁ minutes past 4.
    Or 4 : 38 approx.

  10. Question 10 of 24
    10. Question

    At what time between 5.30 and 6 will the hands of a clock be at right angles?

    Hint

    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 clock-calendar-14950.png
    clock-calendar-14944.png

  11. Question 11 of 24
    11. Question

    At what time between 4 and 5 o’clock will the hands of a watch point in opposite directions?

    Hint

    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 clock-calendar-14938.png
    clock-calendar-14932.png

  12. Question 12 of 24
    12. Question

    At what time between 9’o clock and 10’o clock will the hands of a clock point in the opposite directions?

    Hint

    At 9’o clock, the Minute Hand is ahead of Hour Hand by 15 minutes. The hands will be opposite to each other when there is a space of 30 minutes between them.
    This will happen when the Minute Hand gains 15 minutes’ space over Hour Hand.
    Time taken by Minutes Hand to gain 15 minutes
    clock-calendar-14926.png
    Hence the Hands are opposite to each other at clock-calendar-14920.png minutes past 9.

  13. Question 13 of 24
    13. Question

    At what time between 3 and 4 o’clock, the hands of a clock coincide?

    Hint

    Since, in one hour, two hands of a clock coincide only once, so, there will be value.
    Required time T = clock-calendar-14914.pngminutes past H.
    Here H = initial position of hour hand = 3(Since 3 o’clock)
    A° = required angle = 0°(Since it coincides)
    T = clock-calendar-14907.pngminutes past 3 = clock-calendar-14901.png minutes past 3.

  14. Question 14 of 24
    14. Question

    Find the exact time between 7 am and 8 am when the two hands of a watch meet ?

    Hint

    55 min spaces are gained in 60 min
    ⇒35 min spaces will be gained in 38.18 min.
    ⇒Answer = 7 hrs + 38.18 min.

  15. Question 15 of 24
    15. Question

    How much does a watch lose per day, if its hands coincide every 64 minutes?

    Hint

    55 min. spaces are covered in 60 min.
    60 min. spaces are covered in clock-calendar-15058.pngclock-calendar-15052.png
    Loss in 64 min. clock-calendar-15046.png
    Loss in 24 hrs.clock-calendar-15040.png

  16. Question 16 of 24
    16. Question

    An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?

    Hint

    Angle traced by the hour hand in 6 hours clock-calendar-15034.png

  17. Question 17 of 24
    17. Question

    A clock is set right at 5 a.m. The clock loses 16 min. in 24 hours. What will be the true time when the clock indicates 10 p.m. on the 4th day ?

    Hint

    Time from 5 a.m. on a day to 10 p.m. on 4th day is 89 hours.
    Now, 23 hrs. 44 min. of this clock are the same as 24 hours of the correct clock.
    i.e., ³⁵⁶⁄₁₅ hrs. of this clock = 24 hrs. of correct clock.
    ∴89 hrs. of this clock =clock-calendar-15540.pnghrs. of correct clock
    = 90 hrs of correct clock.
    So, the correct time is 11 p.m.

  18. Question 18 of 24
    18. Question

    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:

    Hint

    Time from 7 a.m. to quarter pas 4
    = 9 hours 15 min.=555 min.
    Now, 37⁄12 min. of this watch = 3 min. of the correct watch.
    555 min. of this watch = clock-calendar-15534.pngmin.
    = clock-calendar-15528.png of the correct watch.
    Correct time is 9 hours after 7 a.m. i.e., 4 p.m.

  19. Question 19 of 24
    19. Question

    A clock gains 15 minutes per day. It is set right at 12 noon. What time will it show at 4.00 am, the next day?

    Hint

    The clock gains 15 min in 24 hours.
    Therefore, in 16 hours, it will gain 10 minutes.
    Hence, the time shown by the clock will be 4.10 am.

  20. Question 20 of 24
    20. Question

    A clock is set right at 1 p.m. If it gains one minute in an hour, then what is the true time when the clock indicates 6 p.m. in the same day?

    Hint

    Time interval indicated by incorrect clock = 6 p.m – 1 p.m = 5 hrs.
    Time gained by incorrect clock in one hour = + 1 min.= + 1/60 hr.
    Using the formula,
    clock-calendar-15124.pngclock-calendar-15118.png
    clock-calendar-15112.png
    ⇒ True time interval clock-calendar-15106.png
    ∴ True time = 1 p.m. + clock-calendar-15100.png hrs. = 5 p.m. + clock-calendar-15094.png hrs.
    = 5 p.m. + clock-calendar-15088.png× 60 min = clock-calendar-15082.pngminutes past 5.

  21. Question 21 of 24
    21. Question

    Two clocks were set right at noon on Sunday. One gains 2 min and the other loses 3 min in 24 hours. What will be the true time when the first clock indicates 3 pm on Wednesday?

    Hint

    Time from noon on Sunday to 3 pm on Wednesday = 75 hours.
    24 hours 2 minutes of the first clock= 24 hours of the correct one.
    ⇒ 1 hour of the first clock= 24 × (30/721) hours of correct one.
    ⇒ 75 hours of the first clock = 24 × 30 × (75/721) hours of correct one
    = 54000/721 hours = 74 hours 53.7 min.
    Hence the answer is 2:54 pm.

  22. Question 22 of 24
    22. Question

    In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hrs. 18 min. 15 seconds of watch time. What is the time gained or lost by this watch in one day?

    Hint

    In a watch than is running correct the minute hand should cross the hour hand once in every clock-calendar-15377.pngmin. So they should ideally cross 3 times once in clock-calendar-15370.pngmin = 196.36 minutes.
    But in the watch under consideration, they meet after every 3hr, 18 min and 15 seconds,
    i.e. clock-calendar-15364.pngmin.
    Thus, our watch is actually losing time (as it is slower than the normal watch). Hence when our watch elapsed clock-calendar-15358.png= 1426.27.
    Hence the amount of time lost by our watch in one day clock-calendar-15352.pngi.e., 13 min and 50s (approx).

  23. Question 23 of 24
    23. Question

    A clock gains 5 minutes. in 24 hours. It was set right at 10 a.m. on Monday. What will be the true time when the clock indicates 10:30 a.m. on the next Sunday ?

    Hint

    Time between 10 a.m. on Mon to 10:30 a.m. on Sun = 144 ½ hrs.
    24 ½ hours of incorrect clock = 24 hours of correct time.
    ∴144 ½ hours of incorrect clock = x hours of correct time.
    ∴x = clock-calendar-15328.png= 144 hours i.e., the true time is 10 a.m. on Sunday.

  24. Question 24 of 24
    24. Question

    A watch which gains uniformly is 2 minutes slow at noon on Monday and is 4 min. 48 sec. fast at 2 p.m. on the following Monday. When was it correct?

    Hint

    Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.
    ∴ The watch gains clock-calendar-15322.png clock-calendar-15316.png
    Now, clock-calendar-15310.pngmin. are gained in 170 hrs.
    ∴ 2 min. are gained in clock-calendar-15304.png
    ∴ 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.

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