What was the day of the week on 15 August 2013?

15th August 2013 = (2013 years + period between 1-1-2013 to 15-8-2013)

odd days in 2000 = 0

in remaining 13 years = (3 leap years + 9 normal years) = (3 * 2 + 9 * 1) = 15 - 14 = 1 odd days

Total number of days in period between 1-1-2013 to 15-8-2013 = 227 days = 32 weeks + 3 days = 3 odd days

Total number of odd days = (1 + 3) = 4 days

Hence, given day is thursday (0 odd day means sunday, 1 odd day means mon and so on )