Calendar Reasoning Tricks & Concepts | Mental Mathematics for Class 8 PDF Download

Days and Week

One week includes following 7 Days :

• Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday
  The days repeat itself after completion of week.

Odd Day 

The remaining days after calculated Completed weeks are odd days. It can be find by divide the number of days from the 7, remainder is Odd Days.

Days of the week start from Monday (1 Jan 0001 was Monday) , Therefore, 1 odd day means Monday.

Tricks – Odd days in a Week -‘0 ‘

• Add or Subtract 7 from any day, you will find same day.
• Like 1 July 2020 is Wed, 8 July 2020 ?
• 1+7 = 8, Therefore, 8 July 2020 is Wednesday

Odd days in Months

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 1: Which of the following is a leap year
(a) 2021
(b) 2022
(c) 2023
(d) 2024
Ans: (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

• 1 st day of the year = Last days of the year
• 1 Jan and 31 Dec will be same day

Example 1: 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 2: 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.

Odd days in 100 and 400 Years

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

Type 1: Day and Month same Year Different

Q1: 12 March 2018 is Sunday. What will be 12 March 2022 ?
Sol:

• 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

Q2: 23 March 1835 is Sunday. What will be 23 March 1882 ?

Sol:

• 1882-1835 = 47 years + 12 LY = 59/7 = 3 OD
• Sunday + 3 = Wednesday

Note: To calculate LY : LY after 1835 is 1836
LY after 18841884 – 1836 = 48/4 = 12 LY

Type -2 : Date and Year Same Month Different

Q1: 04 March 2011 is Sunday. What will be 04 August 2011 ?
Sol:

• Odd day of Mar -3, Apr-2, May-3, Jun-2, July-3 = 13/7 = 6 OD
• Sunday +6 = Saturday

Note : August OD will not be counted.

Type 3: Month and year Same Date Different

Q1: 04 March 2022 is Friday. What will be 30 March 2022 ?
Sol:

• 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= Wednesday

Example 3 : 14 November 2020 is Saturday, What will be the day of 26 January 2026.

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 1: 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
Note : We will subtract the Odd days from the day

Example 2: 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
Century (1900 years ) Odd days = 1 OD
46 (Years)+ 11 (LY)= 57 = 1 OD
Completed Months of 1947 (NY): Jan-3, Feb-0, Mar-3, Apr-2, May-3, Jun-2, Jul-3,
Total OD = 16 = 2 OD
Day of August-15 = 1 OD
Total OD = Century –1 + 46 Years –1 + Months 2 + Days – 1 = 5 OD
15 August 1947 was Friday (5 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)