Explanation:

15 Aug, 1947 = (1946 years + Period from 1.1.1947 to 15.8.1947)
Odd days in 1600 years = 0 
Odd days in 300 years = 1
46 years = (35 ordinary years + 11 leap years) = (35 x 1 + 11 x 2)= 57 (8 weeks + 1 day) = 1 odd day 
Jan.   Feb.   Mar.   Apr.   May.   Jun.   Jul.   Aug = ( 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15 ) = 227 days = (32 weeks + 3 days) = 3 odd days.
Total number of odd days = (0 + 1 + 1 + 3) = 5 odd days. 
Hence, as the number of odd days = 5 , given day is Friday.