Calendar Mathematics
Calendar:- Important Formulas
a) ODD Days :- We should track down the day of the week on a given date.
For this, we utilize the idea of 'odd days'.
In a given period, the quantity of days more than the total weeks are called odd days.
b) Leap Year :-
(I). Consistently separable by 4 is a jump year, on the off chance that it's anything but a long time.
(ii). Each fourth century is a jump year and no other century is a jump year.
Note: A jump year has 366 days. (Leap Year Also Called Jump Year )
Examples: -
Every one of the years 1676, 1948, 2004, etc. is a jump year.
Every one of the years 800, 1200, 1600, 2000 ,etc. is a jump year.
None of the years 2001, 2002, 2003, 2005, 1800 etc. is a jump year.
c) Ordinary Year & Normal Year :-
The year which isn't a jump year is called a normal years. A Normal year year has 365 days.
d) Counting of Odd Days:-
(i) One simple or ordinary year has 365 days = {52 weeks and 1day}
∴ Then the one simple year has 1 odd day .
(ii) One leap year or jump year has 366 days = {52 weeks and 2 days }
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∴ Then the one leap year or jump year year has 2 odd days
(iii) For 100 years there is a = 76 simple or ordinary years + 24 leap year or jump years
∴ There are total odd days = (76 x 1 + 24 x 2) odd days = 124 odd days.
∴ The weeks are 17 and remaining 5 odd days.
# The number of odd days in 100 years = 5 days
The number of odd days in 200 years = { 5🗙 2 } days = 10 days = 1 week + 3 odd days
The number of odd days in 300 years = { 5🗙 3 } days = 15 days = 2weeks + 1 odd day
The number of odd days in 400 years = { 5🗙 4 +1 } days = 21 days = 3weeks + 0 odd day
🍝Likewise, Every single one ofDownload 800 years, 1200 years, 1600 years, 2000 years etc. had 0 odd days.
e) Day of the Week Related to Odd Days:-
Day :- SUN. MON. TUES. WED. THURS. FRI. SUN.
Number of days : - 0 1 2 3 4 5 6
Examples :-
1. If was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2009? | ||||||||||||||||
2. What was the day of the week on 28th May, 2007?
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Answer :- A) Monday
3. What was the day of the week on 17th June, 1999 ? | ||||||||
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Answer :- D) Thursday
4. On what dates of April, 2001 did Monday fall? | ||||||||
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Answer :- B) 2nd, 9th, 16th, 23rd, 30th
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