Days and Week
One week includes the following 7 Days :
Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday
The days repeat itself after completion of the week.
Odd Day
The remaining days after calculated Completed weeks are odd days. It can be found by divide the number of days from the 7, the remainder is Odd Days.
Days of the week start from Monday (1 Jan 0001 was Monday), Therefore, 1 odd day means Monday.
Odd Day 1 2 3 4 5 6 7/0
Day Mon Tue Wed Thu Fri Sat Sun
Tricks - Odd days in a Week -'0 '
Add or Subtract 7 from any day, you will find the same day.
Like 1 July 2020 is Wed, 8 July 2020 ?
1+7 = 8, Therefore, 8 July 2020 is Wednesday
Odd days in Months
Months Days Odd Days
Jan, March, May, July, August, October, December 31 3
February Normal Year 28 0
February Leap Year 29 1
April, June, September, November 30 2
Normal Year
Normal year, which is not divisible by 4 is a Normal Year, However in Century year like 100, 200, 1900, 2000, it should not be divisible by 400.
That means 1900 is divisible by 4 and we may think it a leap year, but it is century year (last two digits 00), we have to divide it by 400.
Hence, it is Normal Year.
Normal Year = 365 day = 52 weeks + 1 day ( 1 Odd Day)
February - 28 days
Leap Year
Leap Year = 366 days = 52 weeks + 2 day ( 2 odd days)
February - 29 days
Example : Which of the following is a leap year
(a) 2021, (b) 2022 (c) 2023 (d) 2024
Answer : (d) 2024 is divisible by 4, therefore it is a Leap Year
Tricks Calendar Reasoning:
First and Last day of a year
In a Normal Year
1st day of the year = Last days of the year
1 Jan and 31 Dec will be same day
Example: 1 Jan 2022 is Saturday, and 31 Dec 2022 is also Saturday
What will be 1 Jan 2023 ?
Normal Year Sat +1 = Sunday
In Leap Year
31 Dec is 1+ 1st Jan Day
Example 1 Jan 2024 is Monday, 31 Dec 2024 = Monday+1 =Tuesday
Months with Same days
When the Number of odd days between any two months in a year is '0', the day of the dates will be same.
Normal Year Jan-Oct Feb-March Feb-Nov Mar-Nov Apr-Jul Sep-Dec
Leap Year Jan-Apr Jan-Jul Feb-Aug Mar-Nov Apr-Jul Sep-Dec
Odd days in 100 and 400 Years
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After 400 Years Calendar repeat itself
1 Jan 2001 – Monday
1 Jan 2401 will Monday
1 Jan 1601 was Monday … etc
Odd days in Century and Last Day
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Type 1: Day and Month same Year Different
12 March 2018 is Sunday. What will be 12 March 2022 ?
Solution :
2018 NY -1
2019 NY -1
2020 LY- 2
2021 NY-1
OD -5 , Sunday +5 = Friday
Trick : 2022- 2018 = 4 Year + 1 LY = 5
23 March 1835 is Sunday. What will be 23 March 1882 ?
Solution
1882-1835 = 47 years + 12 LY = 59/7 = 3 OD
Sunday + 3 = Wednesday
NOTE : To calculate LY : LY after 1835 is 1836
LY after 1884
1884 – 1836 = 48/4 = 12 LY
Type -2 : Date and Year Same Month Different
04 March 2011 is Sunday. What will be 04 August 2011 ?
Solution
Odd day of Mar -3, Apr-2, May-3, Jun-2, July-3 = 13/7 = 6 OD
Sunday +6 = Friday
Note : August OD will not be counted.
Type 3: Month and year Same Date Different
04 March 2022 is Friday. What will be 30 March 2022 ??
Number of days = 30-4 = 26 /7 = 5 OD
Friday +5 = Wednesday
Note : Friday (5) +5 = 10/7 = 3 (Wed)
Type 4: Date, Month, Year all different
Example 1: 11 July 2020 is Saturday, what will be 22 October 2028?
Years : 2028 -2020 = Year- 8 + LY- 2 = 10 , OD -3
Month : July – 3, Aug-3, Sep-2 =8, OD -1 ( Oct will not be counted)
Date : 22-11 = 11, OD = 4
Total OD = 3+1+4 =8 , OD =1
Therefore, Sat +1 = Sunday
Example 2: 15 March 2021 is Monday, What will be 12 July 2023.
Year : 2023-2021 = 2 +0 (LY) = 2 OD
Months : March (31-15 =16) -2 OD, Apr-2, May-3, June-2, July 12 – 5 OD
Months OD : 2 + 2 + 3 + 2 + 5 = 14 = 0 OD
Total OD : Year + Months = 2 + 0= 8 OD -2
Therefore 12 July 2023 will be Monday + 2= Tuesday
Example 3 : 14 November 2020 is Saturday, What will be the day of 26 January 2026.?
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Therefore, 26 January 2026 = Saturday + 2 = Monday
Find the Day of a back date from the given day
When the day of a date is given and day of a date previous to it is asked. We will subtract the odd days from the given day.
Example: 26 January 2020 is on Sunday, What was the day on 26 January 1950.
Years : 2020-1950 – year -70 + LY -17 = 87 – 3 OD
(Including – 2000 CLY, )
Note: For LY 2020 (Before Feb) – 1952 (NLY) = 68/4 =17
26 January 1950 was Sunday (0/7) – 3 = Thursday
Example: 10 Feb 2020 is on Monday, What was the day on 25 December 1918.
Dec 2018, 31 – 25 = 6 OD
Year 2019 NY = 01 OD
Jan 2020 31 days = 3 OD
Feb 2020 , 10 days = 3 OD
Total OD = 6+1+3+3=13 = 6 OD
25 December 1918 was (Monday – 6) = Tuesday
Note : Monday 1+7 – 6 = 2nd day of week
Find the day of a given date
Example 1 : What was the day on 15 August 1947
Completed Year upto 15 Aug 1947 = 1900 + 46
Odd days = 1 (C code) + 46 (Years)+ 11 (LY)= 58 = 2 OD
Completed Months of 1947 (NY): Jan-3,Feb-0, Mar-3, Apr-2, May-3, Jun-2, Jul-3,
Total OD = 15 = 1 OD
Day of August 15 = 1 OD
Total OD = Years 2 + Months 1 + Days 1 = 4
15 August 1947 was Thursday (4 th Day of week)
(Note : Odd day for 300,700,1100,1500,1900,2300.. Century is 1
and Number of LY – 1948 – 1904 = 44/4 =11)
Example 2: Birth date of a student is 25 March 2004, Find the day of that day.
Completed Year : 2000 + 3
Century multiple of 400, code is 0, LY -0
Odd Day = 0 (C Code) + 3 (years) + 0 (LY) =3 OD
Completed Months of 2004 (LY): Jan-3, Feb-1 , = 4 OD
Days 25 = 4 OD
Total OD = 3+4+4 = 11 = 4 OD
25 March 2004 was the Thursday (4 th day of week)
Q 1: Ravi went to see a Movie, 9 day before. He see the Movie only on Friday. Today is what Day of week.
Today = Friday + 9 = Friday + 2 OD = Saturday
Q 2: 29 Feb is Monday. what day was on 11 February.
29, 22, 15 and 8 Feb Monday
8+3 = 11, Monday+3 = Thursday
Q 3 : If this year is a Leap Year and 1 January is Monday. After How Many year 1 Jan will be on Monday.
This Year LY – 1 Jan – Mon
Next Year NY – 1 Jan Wed (2 OD of previous Year)
Next Year NY – 1 Jan Thu (1 OD of previous Year)
Next Year NY – 1 Jan Fri (1 OD of previous Year)
Next Year LY – 1 Jan Sat (1 OD of previous Year)
Next Year NY – 1 Jan Monday (2 OD of previous Year)
After 5 Year
Alternate Method
Add the Odd day of years till it become 7 or multiple of 7.
2 LY + 1 NY + 1 NY + 1 NY + 2 LY = 7 (After 5 years)
Q 4: Ram celebrated his 4th birthday on 29 Feb 2020. When he was born.
4 Birthday 29 Feb 2020
3 Birthday 29 Feb 2016
2 Birthday 29 Feb 2012
Ram Birth Date 29 Feb 2008