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.

17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)
Odd days in 1600 years = 0
Odd days in 300 years = 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.
Jan. Feb. March April May June
(31 + 28 + 31 + 30 + 31 + 17) = 168 days
168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.

Time from 5 a.m on a day to 10 p.m.on 4th day = 89 hours.
Now 23 hrs 44 min. of this clock = 24 hours of correct clock.
Therefore 356 / 15 hrs of this clock = 24 hours of correct clock.
89 hrs of this clock = (24 x (15/356) x 89) hrs
= 90 hrs
So, the correct time is 11 p.m.

Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours.
=170 hours.
The watch gains = (2 + 4 x 4/5) min
= 34/5 min. in 170 hrs.
Now,34/5 min are gained in 170 hrs.
2 min are gained in (170 x 5/34 x 2) hrs.
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.

The total angle traced by the hour hand is the angle traced in 5 hours and 10 minutes.

Angle traced by hour hand in 13/3 hrs = ((360/12) x (13/3))°
=130°
Angle traced by min. hand in 20 min = ((360/60) x 20)°
= 120°
Required angle = (130 – 120)°
= 10°.

In 12 hours, the hands coincide or are in opposite direction 22 times.
Therefore, in 24 hours, the hands coincide or are in opposite direction 44 times a day.

Count the number of odd days from the year 2007 onwards to get the sum equal to 0 odd day.

Year    : 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Odd day : 1    2    1    1    1    2    1    1    1    2    1    

Sum = 14 odd days  0 odd days.

 Calendar for the year 2018 will be the same as for the year 2007.

At 8 o’clock, the hour is at 8 and the minutes 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.

100 years consists 24 leap years and 76 non-leap years.
(100th year is not a leap year if it cannot be divided with 400)