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01. How many times do the hands of a clock coincide in a day?
A. 20 B. 21
C. 22 D. 24

Answer and Explanation

Answer: 22

Explanation:
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, then coincide only once, i.e. at 12 o’clock)


The hands coincide 22 times in a day.

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02. If the hands of a clock coincide every 66 minutes, how much time does the clock gain/loss per day?
A. 11(129/131) B. 14(119/121)
C. 11(109/121) D. 14(109/131)

Answer and Explanation

Answer: 11(109/121)

Explanation:
In a clock showing correct time the hands coincide after every 65 5/11
=> Minutes. If the hands coincide every 66 minutes, it take 66 minutes to cover
     65 5/11 minutes of correct time.
=> It is losing time. It loses 6/11 minutes every 66 minutes.
=> In a day it loses       ( 6/11)
                               66 * (24)(60)

=>  11(109/121) minutes

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03. A clock strikes for every half an hour once and for every hour for the number same as that of the hour. What was the number of strikes given by the clock from 8 hours to 12 hours?
A. 45 B. 50
C. 55 D. 60

Answer and Explanation

Answer: 55

Explanation:
For all half an hour once
Total strikes for half hour = 5
For hour from 8 to 12, number of strikes = 8 + 9 + 10 + 11 + 12 = 50

Total strikes = 5 + 50 = 55

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04. Two clocks are set correctly at 10 am on Friday. The first clock gains 2 minutes per hour and gains twice as much as the second. What time will the second clock register when the correct time is 2 pm on the following Monday.
A. 3 hours 34 min B. 4 hours 3 min
C. 3 hours 16 min D. 3 hours 6 min

Answer and Explanation

Answer: 3 hours 16 min

Explanation:
The time from 10 am Friday to 2 pm the following Monday is 76 hrs. The clock gains 2 min per hour.
∴ Gain in 76 hours = 152 min = 2 hours 32 minutes
∴ Time shown will be 4 hours 32 minutes
Other clock gains 76 min = one hour 16 min
∴ It will show 3 hours 16 min

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05. What is the angle between the hands of a clock at 7:23 am?
A. 83.5° B. 84.5°
C. 80° D. 82°

Answer and Explanation

Answer: 83.5°

Explanation:
θ= 6(x – (11/12)m)°;
x = 35 m.s
m=23 m.s

∴ θ = 6(35 – 11/12 * 23)°
∴ θ = 83.5°

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06. The angle between the minute hand and the hour hand of a clock when the time is 8.30 is
A.  80 degrees B. 75 degrees
C. 60 degrees D. 105 degrees

Answer and Explanation

Answer: 75 degrees

Explanation:
Angle traced by hour hand in 17/2 hours = (360/12 * 17/2) degrees = 255 degrees
Angle traced by minute hand in 30 min = (360/60 * 30) degrees =180 degrees
Hence, Required angle = (255 - 180) degrees = 75 degrees

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07. At 3.40, the hour hand and the minute hand of a clock form an angle of: 

A. 120º B. 125º
C. 130º D. 135º

Answer and Explanation

Answer: 130º

Explanation:

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08. At what time between 4:15 am and 5:05 am will the angle between the hour hand and the minute hand of a clock be the same as the angel between the hands at 8:45 pm? 
A. 23 7/11 minutes past 4 o’clock B. 22 2/11 minutes past 4 o’clock
C. 27 2/11 minutes past 4 o’clock D. 23 2/11 minutes past 4 o’clock

Answer and Explanation

Answer: 23 2/11 minutes past 4 o’clock

Explanation:
We have – θ= 6(40 – 11*45 / 12) = – 30/4. At 8 :45, the angle between the minute hand and the hour hand of the clock will be 30/4°. This is the same as the required angle.
Therefore ±30/4 = 6(20 – 11m/12).
On solving, m=20 m 5/11 minutes or 23 2/11 minutes past 4 o’clock

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09. A clock is started at noon. By 10 mins past 5, the hour hand has turned through
A. 145 degrees B. 150 degrees
C. 155 degrees  D. 160 degrees

Answer and Explanation

Answer: 155 degrees 

Explanation:
Angle traced by hour hand in 12 hours = 360 degrees
Angle traced by hour hand in 5 hours 10 min i.e 31/6 hrs = (360/12 * 31/6) degrees = 155 degrees

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10. The angle between the minute hand and the hour hand of a clock when the time is 4.20 is
A. Zero Degree B. 10 degrees
C. 5 degrees D. 20 degrees

Answer and Explanation

Answer: 10 degrees

Explanation:
Angle traced by hour hand in 17/2 hours = (369/12 * 17/2) = 130 degrees
Angle traced by minute hand in 20 min = (360/60 * 20) = 120 degrees
Hence, Required angle = (130 – 120) degrees = 10 degrees

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