The century divisible by 400 is a leap year.
∴ The year 700 is not a leap year.

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.

There is exactly 1 year, (365 days) between two dates.
2006 is an ordinary year. It has one odd day.
The day of the week on January 12^th 2007 is one day beyond Thursday ⇒ Friday

22 Apr 2222 = (2221 years + period from 1-Jan-2222 to 22-Apr-2222)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2200
= Number of odd days in 200 years
= 5 x 2 = 10 = 3
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
Number of odd days in the period 2201-2221
= 16 normal years + 5 leap years
= 16 x 1 + 5 x 2 = 16 + 10 = 26 = 5 odd days
Number of days from 1-Jan-2222 to 22 Apr 2222
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 22(Apr) = 112
112 days = 0 odd day
Total number of odd days = (0 + 3 + 5 + 0) = 8 = 1 odd day
1 odd days = Monday
Hence 22 Apr 2222 is Monday