The watch gains 5 seconds in 3 minutes => 1 minute in 36 minutes

From 8 AM to 5:15, the incorrect watch has moved 9 hours and 15 minutes = 555 minutes.

When the incorrect watch moves for 37 minutes, the correct watch moves for 36 minutes.

=> When the incorrect watch moves for 1 minute, correct watch moves for 36/37 minutes

=> When the incorrect watch moves for 555 minutes, correct watch moves for (36/37)*555 = 36*15 minutes = 9 hours

=> 9 hours from 8 AM is 5 PM.

=> The correct time is 5 PM.

One hour = 60 min

18/60 = 3/10

Every hour the hour hand and minute hand coincide once.

=> Every 12 hours hands should coincide 12 times

But in 11 to 1 the clock hands coincide once only at 12

Hence, in every 12 hours hands coincide 11 times.

Therefore, In 24 hours clock hands coincide 11 x 2 = 22 times.

Since at 5: 25 the minute hand will be at 5 and the angle between them will be the same as the distance covered in degree by the hour hand in 25 minutes
Required angle = Distance of hour hand = Speed x Time = 1/2 x 25 =12.5 degrees.

At 8 o’clock, the hour is at 8 and the minute’s hand is at 12, i.e., the two hands are 20 min. spaces apart.
So, the minute hand gain = (30 – 20) minutes = 10 minutes
55 minutes will be gained in 60 min.
10 minutes spaces will be gained in ((60/55) x 10) min. = 100/11 min.
The hands will be in the same straight line but not together at 100/11 min. past 8.

Time from 5 AM on a day to 2 PM on 3rd day = 81 hours
In 24 hours, a clock losses 24 minutes
In 81 hours, a clock losses 81 minutes
 At 2 PM, the correct time is 03:21 PM

You can use a short formula to calculate the time when the angle is given

Angle =  (minutes) -30 (hours)

Using the above formula, we get

180 =  (minutes) -30 (hours)

180 =   (minutes) – 30 (6)

180 + 180 =  minutes

Minutes = 2 x 360/ 11

= 65.45

As mentioned in Key Point O, faulty clock will show correct time when it loses or gains 12 Hours.
In the given problem, clock loses 5 Minutes in an hour. So, 1 Minute lost in every 12 minutes (60 minutes / 5 minutes = 12 minutes).
Now, for losing 12 hours i.e. 720 Minutes(12 X 60 = 720) it will take 720 X 12 = 8640 Minutes = 144 Hours = 6 Days.
So, Clock will show correct time after 6 days from 11AM Monday.
Thus, Answer is 11AM on Sunday.

At noon on Sunday watch gains 2 Minutes.
And at 2PM on following Sunday it is 4 Minutes 48 Seconds fast.
So, it gains 6 Minutes 48 Seconds i.e. 2 Minutes + 4 Minutes 48 Seconds (total 408 Seconds) in 170 Hours (Hours from Sunday Noon (12PM) to following Sunday 2PM)
Therefore, watch gains 120 Seconds (2 Minutes) in 170*120/408 = 50 Hours
50 Hours = 2 Days 2 Hours
Thus, Watch was correct after 2 days 2 hours from Sunday noon that is Tuesday 2PM.

Key points – F. It has not been mentioned coincide or opposite of each other. So, we have to consider common scenario where the hands are in straight line that is either opposite or coincide of each other.

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o’clcok only).

So, in a day, the hands point in the opposite directions 22 times.

8 Seconds in 4 Minutes mean 120 Seconds (or 2 Minutes) in one hour.
From 4AM to 11PM (on the same day) = 19 hours
So, total seconds gain in 19 hours = 19 X 120 (Seconds gain per hour) = 2280 Seconds.
Now, 2280 Seconds = 38 Minutes (i.e. 2280/19 = 38)
Thus incorrect clock will show 11:38PM at 11PM.

At 3 o’ clock, the hour hand is at 90 degrees from the vertical.
In 40 minutes,
Hour hand = 90 + 40*(0.5) = 90 + 20 = 110 (The hour hand moves at 0.5 dpm)
Minute hand = 40*(6) = 240 (The minute hand moves at 6 dpm)
Difference or angle between the hands = 240 – 110 = 130 degrees.