A nonleap year (ordinary) consists 365 days => 52 complete weeks and 1 odd day (1 Extra day).
Therefore a nonleap year starts and ends with the same day of the week.
Hence answer is Monday.
A leap year consists 366 days => 52 complete weeks and 2 odd days (2 Extra days).
Therefore if a leap year starts with Friday, then ends with Saturday, i.e day of the week will be 1 day beyond the starting day of the week.
Conventional Method:
Odd days 

Up to 1600 
0 

Up to 1900 [300 yr] 
1 

Up to 1946 
Leap 11 x 2 = 22 Ordinary 35 x 1= 35 
57 (leap + ordinary) 
Till 15/Aug/1947 
227 

Total 
285 
7  )  285 
(  40 
280 

5 
5 = Odd days => 5 = Friday
Direct Method:
15th August 1947 
Odd days 
I] Add Date + Last two digits of the year = 15 + 47

62 
II] Month Code ( August ) 
2 
III] Century Code ( 1900 to 1999) 
0 
Iv] Number of leap year up to 47 ( last two digits of the year) 47/4 
11 
Number of odd days 
75 
7  )  75 
(  10 
70 

5 
(5 odd days, 5 denotes Friday)
26 – January  1950  Odd days  
[i] 26 + 50  =  76  
[ii] January code  =  0  
[iii] Century code  =  0  
[iv] Number of leap years (Up to 50/4)  =  12  
Total  88 
7  )  88 
(  12 
84 

4 
4 = odd days => 4 = Thursday
If on 21st August 2006 is Monday, then on the same date of 2007 will be, one day beyond.
Monday => Monday + 1 day = Tuesday.
If on 21st August 2006 is a Monday, then on the same date of 2005 was, one day behind the given, day of the week, therefore the day of the week on 21/Aug/2005 = Monday – 1 day = Sunday.
We cannot determine without date and month, the day of the week differs, for the days that falls between 1^{st} January to 29^{th} February of a leap year, and 1^{st} March to 31^{st} December of leap year.
As 2016 is a leap year, but on 15^{th} August 2016, leap year does not effect as February 29^{th} is completed, so the day of the week on the same day will be 1^{st} day beyond the given day of the week.
Therefore the day of week = Monday + 1 day = Tuesday.
As 2016 is a leap year, 2015 is ordinary year, from 15^{th} August 2016 to 15^{th} August 2015, we have to cross 29^{th} February of 2016, therefore the day of the week on 15^{th} August 2015 was, 2 days behind Monday, Monday – 2 = Saturday.
For every 400 years or its multiples same calendar repeats, 2816 – 2016 = 800
Therefore on 28^{th} August 2816 the day of the week will be same as on the date of 2016.
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