The Calendar
The Calendar of Class 10
CONCEPT
We are to find the day of the week on a mentioned date. Certain concepts are defined as under.
ODD DAYS
The no. of days exceeding the complete no. of weeks in a duration is the no. of odd days during that duration.
ORDINARY YEAR
An ordinary year has 365 days.
LEAP YEAR
A leap year has 366 days. Every year which is divisible by 4 is called a leap year. For example 1200, 1600, 1992, 2004, etc. are all leap years.

The First year of every century year ending in 00's but not a multiple of 400 is not considered a leap year. For example 900,1000, 1100, 1300, 1400, 1500, 1700, 1800, 1900, 2100 are not leap years. 
COUNTING OF ODD DAYS
(i) Every Ordinary year has 365 days = 52 weeks + 1 day ∴ (ordinary year has 1 odd day).
(ii) Every leap year 366 days = 52 weeks + 2 days ∴ (leap year has 2 odd days).
(iii) 100 years = 76 ordinary years + 24 leap years ( The year 100 is not a leap year)
= 76 odd days + 2 × 24 odd days = 124 odd days.
124/7 = 5 (Remainder) = 05 odd days
Similarly, 200 years = 10 odd days = 03 odd days
300 years = 15/7 = 01 odd day
400 years = 20 + (1)/7 = 0 odd day {1 is added as 400 is a leap year}
Similarly, 800, 1200, 1600, 2000, 2400 years contain 0 odd days
COUNTING OF DAYS
After counting the odd days, we find the day according to the no. of odd days → Sunday for 0 odd day, Monday for 01 odd day and so on.

In an Ordinary Year, First & last day of the year are the same. (i) If 1 Jan is Friday than 31 Dec. will also have Friday. (ii) For a leap year, if first day is Monday then last day will be Tuesday for the same year. (iii) Calendar year 1 Jan to 31 Dec. Financial year 1 April to 31 March. (iv) The day on which calendar Started i.e., 1 Jan, 001 was Monday. (v) In a Leap year, February is of 29 days. In an ordinary year, February has 28 days 
YEAR TABLE
Ordinary Year – 365 days 
Leap Year – 366 days 

January 
31 
January 
31 
February 
28 
February 
29 
March 
31 
March 
31 
April 
30 
April 
30 
May 
31 
May 
31 
June 
30 
June 
30 
Total 
181 days 
Total 
182 days 
July 
31 
July 
31 
August 
31 
August 
31 
September 
30 
September 
30 
October 
31 
October 
31 
November 
30 
November 
30 
December 
31 
December 
31 
Total 
184 days 
Total 
184 days 
CALCULATING ODD DAYS
Month 
Jan 
Feb 
March 
April 
May 
June 
July 
Aug 
Sep 
Oct 
Nov 
Dec 
Odd days 
3 
0/13 ord./Leap yr 
3 
2 
3 
2 
3 
3 
2 
3 
2 
3 
Months of years 
I^{st} three months (1 Jan to 31 March) 
II^{nd} three months (1 Apr to 30 June) 
III^{rd} three months (1 July to 30 Sep.) 
IV^{th} (last) three months 
Total year (1 Jan. to 31 Dec.) 
Total days 
90 / 91 ord. / leap 
91 
92 
92 
365/366 ord./leap 
Odd days 
6 / 0 ord. / leap 
0 odd day 
1 odd day 
1 odd day 
1 / 2 odd days 