15^th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)

Odd days in 1600 years = 0

Odd days in 400 years = 0

9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days \(\equiv\) 4 odd days.

Jan.  Feb.   March    April    May  June  July  Aug.

(31 +  28  +  31   +   30   +  31  + 30  + 31  + 15) = 227 days

So, 227 days = (32 weeks + 3 days) \(\equiv\) 3 odd days.

Total number of odd days = (0 + 0 + 4 + 3) = 7 \(\equiv\) 0 odd days.

Given day is Sunday.