At first be patients and read carefully the following
Leap year: A year which is not a century and is divisible by 4 is called a leap year. Also, every 4th century is a leap year. For example, 1856,1952,2008,400,1200,1600 etc.are leap year. A leap year has 366
days
Ordinary Year: A year which is not a leap year is called ordinary year. For example, 1851,1957,2007,1800,2015 etc. are ordinary years. An ordinary year has 365 days.
Odd days: The no of day more than the complete weeks in a given period is called odd days.
Calculation of odd days:
One Ordinary year=365days=(52week+1day)
Therefore, 1 Ordinary year has 1 odd day.
One leap year=366 days=(52weeks+2days)
Therefore, 1 leap year has 2 odd days.
One century=100 years=76 ordinary year+24 leap years
=(76×1+24×2) odd days
=124 odd days
=17weeks+5days
=5 odd days
Therefore, number of odd days in 100 years=5
Hence, number of odd days in 200 years=5×2 days=10 days=1
Week+3 days=3 odd days
Number of odd days in 300 years=5×3 days=15 days=2 weeks+1day= 1 odd day.
Number of odd days in 400 years= (5×4+1) days=21 days=0 odd day.
Similarly, each of the centuries 800 years, 1200 years, 1600 years, 2000 years, 2800 years etc. has 0 odd days. Thus, every 4th century has 0 odd days.
Relation between odd days and days of a week:
Odd day’s number Days of a week
0 Sunday
1 Monday
2 Tuesday
3 Wednesday
4 Thursday
5 Friday
6 Saturday
Example: It was Tuesday on 1st January, 2008. What was the day of the week on 1st January, 2011?
Answer: On 31st December, 2007 it was Monday.
Number of odd days for the year 2008=2(since 2008 is a leap year)
Number of odd days for the year 2009=1 (since 2009 is an ordinary years)
Number of odd days for the year 2010=1 (since 2010 is an ordinary years)
Therefore, number of odd days from year 2008 to the year 2010=(2+1+1)=4 days.
Hence, on 31st December 2010, it was Friday (4 days ahead of Monday, because on 31st December,2007, it was Monday).
Therefore, on 1st January, 2011 it was Saturday.
