Clocks Calender and Age

q = 11/2 m – 30h = 11/2 *30 - 30 *5 = 165-150 = $15^\circ$

18*2 *6 = 216 degree

The number of hours from 8:00 p.m. on Thursday to 8:00 a.m. on Monday = 84 hours. In 84 hours, the clock gained 12 minutes. But to show the correct time, the clock has to gain 5 minutes. :. 5/12 *84 = 35 hours. 35 hours from 8:00 p.m. on Thursday is 7:00 a.m. on Saturday.

$3960/(360*2) = 5.5^\circ$

42*6-(42/2) = 252-21 = 231 degree

Odd days from March to October : 3 + 2 +3 +2 +3 +3 +2 +3 = 21/7 = 0 . If odd day is 0 then next month has the same calendar.

730/7 = 2 odd days. So Saturday will be the day of the week.

It is a leap year. So 16(Jan)+ 29(Feb) + 15(March) = 60 days

100 years contains 5 odd days. So last day of 1st century is ‘Friday’. 200 years contains (5*2) =10 = 3 odd days. So last day of second century is ‘Wednesday’. 300 years contain 15 odd days = 1 odd day. . : Last day of 3rd century is ‘Monday’. 400 years contains 0 odd day. : . Last day of 4th century is ‘Sunday’. Since the order is continually kept in successive cycles, we see that the last day of a century cannot be Tuesday, Thursday or Saturday

2000 years have 2 odd days. Number of odd days from 2001 –2009 = 11 odd days = 4 odd days. 1st January. 2010 has 1 odd day. Total number of odd days = (2 + 4 + 1) = 7 = 0 odd day : . 1st January, 2010 will be a Sunday.