If the period between the two months is divisible by 7, then that two months will have the same calender .
(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.
We know that,
Odd days --> days more than complete weeks
Number of odd days in 400/800/1200/1600/2000 years are 0.
Hence, the number of odd days in first 1600 years are 0.
Number of odd days in 300 years = 1
Number of odd days in 49 years = (12 x 2 + 37 x 1) = 61 days = 5 odd days
Total number of odd days in 1949 years = 1 + 5 = 6 odd days
Now look at the year 1950
Jan 26 = 26 days = 3 weeks + 5 days = 5 odd days
Total number of odd days = 6 + 5 = 11 => 4 odd days
Odd days :-
0 = sunday ;
1 = monday ;
2 = tuesday ;
3 = wednesday ;
4 = thursday ;
5 = friday ;
6 = saturday
Therefore, Jan 26th 1950 was Thursday.
How to find the years which have the same Calendars :
Leap year calendar repeats every 28 years.
Here 28 is distributed as 6 + 11 + 11.
Rules:
a) If given year is at 1st position after Leap year then next repeated calendar year is Given Year + 6.
b) If given year is at 2nd position after Leap year then next repeated calendar year is Given Year + 11.
c) If given year is at 3rd position after Leap year then next repeated calendar year is Given Year + 11.
Now, the given year is 2018
We know that 2016 is a Leap year.
2016 2017 2018 2019 2020
LY 1st 2nd 3rd LY
Here 2018 is at 2 nd position after the Leap year.
According to rule ( b) the calendar of 2018 is repeated for the year is 2018 + 11 = 2029.
We already know that the calendar after a leap year repeats again after 28 years.
Here 1988 is a Leap year, then the same calendar will be in the year = 1988 + 28 = 2016.
If yesterday were tomorrow, today is Friday => tomorrow of friday is Saturday.
Hence, it implies that today is Sunday if tomorrow is Saturday.
Given that the month begins on a Friday and has 31 days
Sundays = 3rd, 10th, 17th, 24th, 31st
=> Total Sundays = 5
Every second & fourth Saturday is holiday.
2nd & 4th Saturday in every month = 2
Total days in the month = 31
Total working days = 31 - (5 + 2) = 24 days.
350 days = (350/7=50 weeks) i.e No odd days,
So it will be a Saturday.
Calculating Age has 2 conditions. Let your Birthday is on January 1st.
1. If the month in which you are born is completed in the present year i.e, your birthday, then
Your Age = Present year - Year you are born
As of now, present year = 2018
i.e, Age = 2018 - 1995 = 23 years.
2. If the month in which you are born is not completed in the present year i.e, your birthday, then
Your Age = Last year - Year you are born
As of now, present year = 2018
i.e, Age = 2017 - 1995 = 22 years.
We know that the day repeats every 7 days, 14 days, 21 days,...
So if today is Monday, after 7 days it is again Monday, after 14 days again it is Monday.
Hence, after 2 weeks i.e, 14 days the day repeats and is the same day.
Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.
On 1st Jan 2006, it was Sunday.
Thus, On 1st Jan, 2010 it is Friday.
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