15^th 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.

16^th July, 1776 = (1775 years + Period from 1^st Jan, 1776 to 16^th July, 1776)
Counting of odd days :
1600 years have 0 odd day
100 years have 5 odd days
75 years = (18 leap years + 57 ordinary years)
= [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days)
= 2 odd days
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day
Jan   Feb   Mar   Apr   May   Jun   Jul
31 + 29 + 31 + 30 + 31 + 30 + 16
= 198 days
= (28 weeks + 2 days)
Total number of odd days = (0 + 2) = 2
Required day was ‘Tuesday’.

This can be illustrated with an example.
Ex: 1896 is a leap year.The next leap year comes in 1904 (1900 is not a leap year).

Explanation : The length of the solar year, however, is slightly less than

days-by about 11 minutes. To compensate for this discrepancy, the leap year is omitted three times every four hundred years.

In other words, a century year cannot be a leap year unless it is divisible by 400. Thus 1700, 1800, and 1900 were not leap years, but 1600, 2000, and 2400 are leap years.

Given year is divided by 4, and the quotient gives the number of leap years.
Here, 100 ÷ 4 = 25
But, as 100 is not a leap year ⇒ 25 – 1 = 24 leap years.

If the period between the two months is divisible by 7, then that two months will have the same calendar.
(a). Oct + Nov = 31 + 30 = 61 (not divisible by 7)
(b). Apr + May + Jun + Jul + Aug + Sep + Oct = 30 + 31 + 30 + 31 + 31 + 30 + 31 = 214 (not divisible by 7)
(c). Jun + July + Aug + Sep = 30 + 31 + 31 + 30 = 122 (not divisible by 7)
(d). Apr + May + June = 30 + 31 + 30 = 91 (divisible by 7)
Hence, April and July months will have the same calendar.

Given year is divided by 4, and the quotient gives the number of leap years.
Here, 300 ÷ 4 = 75
But, as 100, 200 and 300 are not leap years ⇒ 75 – 3 = 72 leap years.

Let us find the day on 1^st July, 2004.
2000 years have 0 odd day. 3 ordinary years have 3 odd days.
Jan.   Feb.   March   April   May   June   July
31 + 29 + 31 + 30 + 31 + 30 + 1
= 183 days
= (26 weeks + 1 day)
Total number of odd days = (0 + 3 + 1) odd days = 4 odd days.
∴ 1^st July 2004 was ‘Thursday’
Thus, 1^st Monday in July 2004 as on 5^th July. Hence, during July 2004, Monday fell on 5th, 12th, 19th and 26th.

First,we count the number of odd days for the left over days in the given period.
Here,given period is 12.2.1986 to 1.1.1987
Feb   Mar   Apr   May   June   July   Aug   Sept   Oct   Nov   Dec   Jan
16   31   30   31   30   31   31   30   31   30   31   1 (left days)
2 + 3 + 2 + 3 + 2 + 3 + 3 + 2 + 3 + 2 + 3 + 1(odd days)
= 1 odd day
So, given day Wednesday + 1 = Thursday is the required result.