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 \(\equiv\) 0 odd days.

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

The century divisible by 400 is a leap year.

So,  The year 700 is not a leap year.

The year 2006 is an ordinary year. So, it has 1 odd day.

So, the day on 8^th Dec, 2007 will be 1 day beyond the day on 8^th Dec, 2006.

But, 8^th Dec, 2007 is Saturday.

So, 8^th Dec, 2006 is Friday.

The year 2008 is a leap year. So, it has 2 odd days.

1^st day of the year 2008 is Tuesday (Given)

So, 1^st day of the year 2009 is 2 days beyond Tuesday.

Hence, it will be Thursday.

The year 2007 is an ordinary year. So, it has 1 odd day.

1^st day of the year 2007 was Monday.

1^st day of the year 2008 will be 1 day beyond Monday.

Hence, it will be Tuesday.

Angle traced by the hour hand in 6 hours = \(\left(\frac{360}{12}\times6\right)^{0} = 180^{0} \)

Angle traced by hour hand in  \(\frac{125}{12}\)  hrs =\(\left(\frac{360}{12}\times\frac{125}{12}\right)^{0}= 312\frac{1}{2}^{0}\)

Angle traced by minute hand in 25 min = \(\left(\frac{360}{50}\times25\right)^{0}=150^{0}\)

So, Reflex angle = 360º – \(\left( 312\frac{1}{2}^{0}-150\right)^{0}=360^{0}-162\frac{1}{2}^{0}=197\frac{1}{2}^{0}\)

Angle traced by hour hand in 12 hrs = 360º.

Angle traced by hour hand in 5 hrs 10 min. i.e.,  \(\frac{31}{6}hrs=\left(\frac{360}{12}\times\frac{31}{6}\right)^{0}= 155^{0} \)

Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. = \(\frac{37}{4}\)

3 min. 5 sec. of this clock = 3 min. of the correct clock.

      \(\frac{37}{720}\)  hrs of this clock =  \(\frac{1}{20}\)  hrs of the correct clock.

   \(\frac{37}{4}\) hrs of this clock =   \(\left(\frac{1}{20}\times\frac{720}{37}\times\frac{37}{4}\right)\)  hrs of the correct clock

= 9 hrs of the correct clock.

So, The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.

55 min. spaces are covered in 60 min.

60 min. spaces are covered in \(\left(\frac{60}{55}\times60\right)min.=65\frac{5}{11}min\)

Loss in 64 min. = \(\left(65\frac{5}{11}-64\right)=\frac{16}{11}min\)

Loss in 24 hrs = \(\left(\frac{16}{11}\times\frac{1}{64}\times24\times60\right)min.=32\frac{8}{11}min\)