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.

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

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

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

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°

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

Answer: 130º

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

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

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