Calendar – Railway Reasoning

If the period between the two months is divisible by 7, then that two months will have the same calendar.
( April, july ) ⇒ april + may + june = 30 + 31 + 30 = 91 (divisible by 7) (October, december)
⇒ october + november = 31 + 30 = 61 (not divisible by 7)
( April, november )
⇒ april + may + june + july + august + september + october
= 30 + 31 + 30 + 31 + 31 + 30 + 31 = 214 (not divisible by 7)
(June, october)
⇒ june + july + august + september
= 30 + 31 + 31 + 30 = 122
(not divisible by 7)Hence April and July have the same calendar.

Formula for calculating day of any date 0 = sunday, 1 = monday ….
6 = saturday A = century code (4,2,0,6 for remainder 1,2,3,0) dividing first two digits of the year by 4, B = last two digits of year, C = number of leap years fallen in that century before that date, D = month code (respective code of the months are 0,3,3,6,1,4,6,2,5,0,3,5) E = date, Day = remainder of (A + B + C + D + E) when divided by 7. For 26 January 1989
A = 0, B = 89, C = 22, D = 0, E = 26
A + B + C + D + E = 137,137 divided by 7 gives remainder as 4, 4 means Thursday.

Since 3ʳᵈ January 2018 was a Wednesday. Therefore,
3ʳᵈ January 2019 = Thursday
3ʳᵈ January 2020 = Friday (since 2020 is  a leap year, it has 365+1 days, therefore,
3 jan 2020 = Friday)
3ʳᵈ January 2021 = Sunday
3ʳᵈ January 2022 = Monday
3ʳᵈ January 2023 = Tuesday
3ʳᵈ January 2024 = Wednesday

Aizaz was born on 5 January 2015 .
Adding 365 day , now the date will be 5 January 2016.
Now, 553 - 365 = 188 days
Now from 5 january 2016
26 + 29 + 31 + 30 + 31 + 30 = 177
Now we reached 30 June 2016.
188 - 177 = 11 days
Now the date is 11 july 2016.
The correct answer is 11 july 2016.

Formula for calculating day of any date
0 = sunday, 1 = monday.... 6 = saturday
A = (4,2,0,6 for remainder 1,2,3,0)dividing by first two digit of the year by 4
B = last two digits of year
C = number of leap years fallen in that century before that date.
D = month code (respective code of the months are 0, 3, 3, 6, 1, 4, 6, 2, 5, 0, 3, 5)
E = date
Day = remainder of (A + B + C + D + E) when divided by 7.
NOTE:- Leap Year Code : The other thing to take into account is whether you are
dealing with a leap year.
EDIT: If the date is in January or February of a leap year , you have to subtract one
from your total before the final step.
For 10 January 2012,
A= 6, B= 12, C= 3, D= 0, E= 10
So, This year is a Leap year (by using leap year code):
Total= A + B + C + D + E - 1 = 6 + 12 + 3 + 0 + 10 - 1 = 30.
Day code = Remainder of (Total/7) = 2.
Since, 2 stands for Tuesday.

Formula for calculating day of any date
0= sunday, 1=monday.... 6 saturday
A = century code (4, 2, 0, 6 for remainder 1, 2, 3, 0)dividing first two digit of the
year by 4
B = last two digits of year
C = number of leap years falling in that century before that date.
D= month code (respective code of the months are 0, 3, 3, 6, 1, 4, 6, 2, 5, 0, 3, 5)
E = date
Day = remainder of (A + B + C + D + E) when divided by 7.
For 10 January 2006
A = 6, B = 06, C = 1, D = 0,E = 10
A + B + C + D + E = 23
On dividing 23 by 7, remainder = 2
2 means Tuesday.

No of days between 10 august and 18 september = 39
No of odd days = 39/7 = 4 odd days
So, Tuesday + 4 = Saturday

5 March 2009 - Thursday
5 March 2010 - Friday
5 March 2011 - Saturday
5 March 2012 - Sunday
5 March 2013 - Tuesday
5 March 2014 - Thursday
5 March 2015 - Friday
5 March 2016 - Saturday
Again 5 March to 11 March = 6 days
So, Saturday + 6 days = Friday

In Ordinary year (+1)
5 august 2012 = sunday ,then
5 august 2013 = monday
5 august 2014 = tuesday
5 august 2015 = wednesday
Odd days between 5 august 2015 to 17 september 2015

Wednesday + 1 = thursday

Today = Thursday
560 days from today ,Number of odd days = 560 ÷ 7 = 0
So, it will be Thursday after 560 days.