The Calendar
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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.
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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.
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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
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Ordinary Year – 365 days |
Leap Year – 366 days |
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January |
31 |
January |
31 |
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February |
28 |
February |
29 |
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March |
31 |
March |
31 |
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April |
30 |
April |
30 |
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May |
31 |
May |
31 |
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June |
30 |
June |
30 |
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Total |
181 days |
Total |
182 days |
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July |
31 |
July |
31 |
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August |
31 |
August |
31 |
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September |
30 |
September |
30 |
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October |
31 |
October |
31 |
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November |
30 |
November |
30 |
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December |
31 |
December |
31 |
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Total |
184 days |
Total |
184 days |
CALCULATING ODD DAYS
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Month |
Jan |
Feb |
March |
April |
May |
June |
July |
Aug |
Sep |
Oct |
Nov |
Dec |
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Odd days |
3 |
0/13 ord./Leap yr |
3 |
2 |
3 |
2 |
3 |
3 |
2 |
3 |
2 |
3 |
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Months of years |
Ist three months (1 Jan to 31 March) |
IInd three months (1 Apr to 30 June) |
IIIrd three months (1 July to 30 Sep.) |
IVth (last) three months |
Total year (1 Jan. to 31 Dec.) |
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Total days |
90 / 91 ord. / leap |
91 |
92 |
92 |
365/366 ord./leap |
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Odd days |
6 / 0 ord. / leap |
0 odd day |
1 odd day |
1 odd day |
1 / 2 odd days |
