A Calendar is a chart or series of pages showing the days, weeks, and months of a particular year, or giving particular seasonal information.
The leap year occurs every four years, most of the time, but there are scenarios where the gap between two leap years was 8 years instead of the regular 4 years.
Example: The year 1896 is a leap year. The next leap year comes in 1904 (1900 is not a leap year).
In order to make the investigation easier and faster, any year which is divisible by number 4 completely (remainder becomes zero) is considered as a leap year.
Example: 1888, 2012, 2016 are leap years as it’s completely divisible by 4. Years like 2009, 2019 etc. are not divisible by 4 completely hence they normal years.
An exception to note:
A year 700 is completely divisible by 4, but it is not considered as a leap year. For a century year, the logic follows that it should always be divisible by 400 not by 4. Even though the year 700 is divisible by 4 but not by 400. Hence, the year 700 cannot be considered as a leap year.
Example: 400, 800, 1200 etc. are leap years as they are divisible by 400 and years 300, 700, 100 etc. are not leap years as they are not divisible by 400.
The year consists of 365 days, 5 hours, 48 minutes (52 weeks and 1 odd day). An extra day is added once in every fourth year which was called the leap year, which has 366 days (52 weeks and 2 odd days).
To find the day of any given date of the year, you need to understand the calendar calculations:
Q2: If today is Sunday, what will be the day on 7777th day?
Sol: If today is Sunday, then the 7th day from today will be Sunday.
Similarly, the 14th day, 21st day or 70th day or 700th day or 7000th day or 7777th day will be Sunday.
Hence, the answer is Sunday.
In this section, one has to find out the day of the week of a given date. There will no reference date or day has given here. One can make use of the concept of an odd day to find the answer.
Q1: What day of the week was 15th August 1947?
Sol: The date August 15th 1947 can be divided as follows for easy calculation:
1600 years + 300 years+ 46 years (1901 to 1946) + Jan 1st to august 15th (of 1947)
Note: Do not write 47 years in the third section, it would indicate 47th year in that century is over.
1600 years + 300 years+ 46 years (1901 to 1946) + Jan 1st to august 15th (of 1947)
Now let’s find out the total number of odd days in each section:
Section 1: 1600 is a multiple of 400 years. 400 years have 0 odd days hence 1600 years should have 0 odd days.
Section 2: The second section 30 years will have 1 odd day. Kindly refer to “evaluation of odd days in a century” topic for clarification.
Section 3: This section has 46 years from 1901 to 1946, we know that an ordinary year has one odd day and a leap year has 2 odd days.
Let’s first calculate the total number of leap years from 1901 to 1946.
Division of 46 by 4 gives the quotient as 11, which indicates that from 1901 to 1946 we have 11 leap years. If there are 11 leap years among 46 years then remaining 35 years should be ordinary years. Hence, 35 ordinary years will have 35 odd days and 11 leap years will have 11*2 = 22 years.
The total number of odd days in 46 years will be 35+22 = 57 odd days. The division of 57 by 7 given the remainder as 1.This indicates from 1901 to 1946 there is only one odd day.
Section 4: It has months from January to August 15th. We have already calculated the total number of odd days in each month in the odd day’s section.
Since 1947 is not a leap year February had zero odd days.
Check the table below for a better understanding of the number of odd days in a month:
The total number of odd days is 31 which when divided by 7 gives the remainder 3. Hence, the total number of odd days in the year 1947 from January 1st to August 15th is 3.
Adding the total number of odd days of each section:
The total number of odd days = 0 + 1 + 1 + 3 = 5 = Friday. Hence, August 15th 1947 was Friday.
Question: Which year in the future will have the same calendar exactly as 2009?
(A) 2010
(B) 2013
(C) 2015
(D) 2017
Ans: (C)
So: If the total number of odd days between any years is zero or it’s a multiple of seven. Then, those two years will have the same calendar.
The total number of odd days is listed below:
Hence, 2015 will have the same calendar as 2009. Option C is the correct answer.
Example 1: What was the day on 9^{th} February 1979?
 You know that in 1600 years, there will be 0 odd days. And in the next 300 years, there will be 1 odd day.
 From 1901 to 1978 we have 19 leap years and 59 nonleap years. So, the total number of odd days up to 31st Dec.
 1978 is 19 x 2 + 59 = 97. On dividing 97 by 7 we get 6 as the remainder, which is the total number of odd days in these years.
 So, till 31^{st} Dec. 1978, we have 1 + 6 = 7 odd days, which forms one complete week.
 Now, in 1979, we have 3 odd days in January, and 2 odd days in the month of February (up to 9^{th} Feb). So, the total odd days are 3 + 2 = 5.
 Hence, 9^{th} February 1979 was a Friday.
Example 2: If May 10, 1997, was a Monday, what will be the day on Oct 10, 2001?
 In this question, the reference point is May 10, 1997, and you have to find the number of odd days from May 10, 1997, up to Oct 10, 2001.
 Now, from May 11, 1997  May 10, 1998 = 1 odd day
May 11, 1998  May 10, 1999 = 1 odd day
May 11, 1999  May 10, 2000 = 2 odd days (2000 was leap year)
May 11, 2000  May 10, 2001 = 1 odd day Thus, the total number of odd days up to May 10, 2001 = 5.
 Now, the remaining 21 days of May will give 0 odd days. In June, we have 2 odd days; in July, 3 odd days; in August, 3 odd days; in September, 2 odd days and up to 10^{th} October, we have 3 odd days.
 Hence, total number of odd days = 18 i.e. 4 odd days. Since, May 10, 1997 was a Monday, then 4 days after Monday will be Friday. So, Oct 10, 2001, would be a Friday.
Example 3: If 11th April 1911 was a Tuesday, what would be the day on 17^{th} September 1915?
 Firstly in terms of years, the year 1911 to 1912 would give us 2 odd days and 1913, 1914, 1915 would give 1, 1 and 1 odd day respectively.
 Now shift the focus on months. If you move one month ahead i.e. from 11th April to 11th May, the month ending in between is April, which gives you 2 days. Now after that, the month of May, June, July, and August gives you 3, 2, 3, and 3 odd days respectively.
 With this, you reach on 11th September 1915. After this, there are 6 more September days (from 11th to 17th September).
 The total number of odd days is 2 + 1 + 1 + 1 + 2 + 3 + 2 + 3 + 3 + 6 = 24.
 Subtracting 21 (3 full weeks) from this the odd number of days left is 3. Adding three days to the day given i.e. Tuesday, the answer becomes Friday.
Example 4: If 15 March 1816 was Friday, what day of the week would 15th April 1916 be?
 We are given that 15th March 1816 was a Friday.
 Now we know that 100 years have 5 odd days. So till 15th March 1916, we will be having 5 odd days. So if we move from 15th March 1816 to 15th March 1916, we will encounter 5 odd days.
 Now from 15th March 1916 to 15th April 1916 there would be 3 odd days.
 So total number of odd days = 5+3 =8
8 mod 7 = 1
So, 15th April 1916 would be Friday + 1= Saturday
Example 5: The leap year 1895 is having the same calendar as that of the year X. Which of the following is a possible value of X.
 1895 is not a leap year.
 So, it will have 1 odd day.
 Since, 1896 is a leap year, it will add 2 odd days.
 Similarly, 1987, 1898, 1899, 1900 will add 1,1,1,1 odd days.Now the total number of odd days add up to 7.
 So, the next year 1901 will have the same calendar as 1895.
207 videos156 docs192 tests

1. What is the importance of calendarbased questions in exams? 
2. What is the basic structure of a calendar? 
3. What are odd days in a calendar? 
4. What is a leap year? 
5. How can calendar calculations be solved? 
207 videos156 docs192 tests


Explore Courses for UPSC exam
