Calendar Reasoning Tricks: Odd Days, Leap Year and Day Finding Questions for SSC CGL, CHSL

A calendar reasoning question asks you to find the day of a given date, such as "What was the day on 15 August 1947?", or the day after some number of days. The rule is simple: divide the days by 7 and use the remainder, which is called the number of odd days. These calendar reasoning tricks for SSC give the odd day tables, the leap year rule, the repeating calendar facts and solved examples.

Basic Facts

• A week has 7 days, so the days repeat after every 7 days.
• Odd days are the days left over after taking out complete weeks. Example: 15 days = 2 weeks + 1 odd day.
• An ordinary year has 365 days = 52 weeks + 1 odd day.
• A leap year has 366 days = 52 weeks + 2 odd days.

Leap Year Rule

• A year that is divisible by 4 is a leap year, such as 2024.
• A century year must be divisible by 400 to be a leap year. So 2000 was a leap year, but 1900 and 2100 are not.

Odd Days in Centuries

After 400 years the calendar repeats, so the count for 1600, 2000 and 2400 is zero.

Odd Days in Months

Day Code

Steps to Find the Day of a Date

1. Count the odd days of the complete centuries before the year (1600 years = 0, 1700 = 5 ... use the table).
2. Count the odd days of the complete years in the last century: odd days = years + number of leap years.
3. Add the odd days of the complete months of that year.
4. Add the days of the given date and take the remainder after dividing by 7.
5. Add all the odd days and use the day code.

Solved Examples

Example 1. Find the day on 15 August 1947.
1900 years give 1 odd day (1600 gives 0 and 300 give 1). From 1901 to 1946 there are 46 years with 11 leap years, so 46 + 11 = 57, which leaves 1 odd day. January to July 1947 have 3 + 0 + 3 + 2 + 3 + 2 + 3 = 16, which leaves 2 odd days. The 15 days leave 1 odd day. The total is 1 + 1 + 2 + 1 = 5, which is Friday.

Example 2. If today is Monday, what will be the day after 100 days?
100 ÷ 7 leaves a remainder of 2. Monday + 2 days = Wednesday.

Example 3. If 1 January 2024 was a Monday, what was the day on 1 January 2025?
2024 is a leap year with 2 odd days. Monday + 2 = Wednesday.

Example 4. The calendar of which year is the same as 2017?
From 2017 to 2022 the odd days are 1 + 1 + 1 + 2 (2020 is leap) + 1 + 1 = 7, which is 0. So the calendar of 2023 is the same as 2017.

Useful Tricks

• The 1st, 8th, 15th, 22nd and 29th of a month fall on the same day.
• In any month, the 29th, 30th and 31st fall on the same weekdays as the 1st, 2nd and 3rd.
• In a leap year, the last day of the year is one weekday after the first day (2024 began on Monday and ended on Tuesday).
• In an ordinary year, the first and the last day of the year are the same weekday (2023 began and ended on Sunday).

Quick Tips

• Memorise the day code: Sunday is 0 and Saturday is 6.
• Learn the odd days of the centuries: 5, 3, 1 and 0.
• Count the leap years carefully when you count the odd days of the years.
• Always add the date as a number of days at the end.

Quick Revision Points

• Ordinary year = 1 odd day. Leap year = 2 odd days.
• 100 years = 5 odd days and 400 years = 0 odd days.
• A century year is a leap year only if it is divisible by 400.
• Day code: Sunday 0, Monday 1 ... Saturday 6.
• The calendar of 2017 repeats in 2023.

Practice Questions With Answers

1. How many odd days are there in 100 years?
   Answer: 5
2. How many odd days are there in 400 years?
   Answer: 0
3. How many odd days are there in an ordinary year?
   Answer: 1
4. How many odd days are there in a leap year?
   Answer: 2
5. What was the day on 15 August 1947?
   Answer: Friday
6. If 5 September 2023 was a Tuesday, what was the day on 5 October 2023?
   Answer: Thursday
7. Is the year 2000 a leap year?
   Answer: Yes, because 2000 is divisible by 400
8. The calendar of which year is the same as that of 2017?
   Answer: 2023
9. If today is Saturday, what will be the day after 50 days?
   Answer: Sunday
10. What was the day on 26 January 1950?
    Answer: Thursday

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Reasoning notes page, read the previous topic Puzzle Reasoning and the next topic Clock Angle Reasoning.

Frequently Asked Questions

What are odd days?

Odd days are the days left after taking out complete weeks from the total number of days.

How many odd days are there in a leap year?

A leap year has 2 odd days.

How do I check a leap year?

A year is a leap year if it is divisible by 4, and a century year must be divisible by 400.

Is 1900 a leap year?

No. 1900 is a century year that is not divisible by 400.

How many odd days are there in 200 years?

There are 3 odd days in 200 years.

What is the day code for Sunday?

Sunday has the code 0.

How do I find the day after n days?

Divide n by 7, and move that many days ahead of the given day.

How do I find the day of a past date?

Add the odd days of the centuries, the years, the months and the date, and then use the day code.

When does a calendar repeat?

It repeats when the total odd days between two years are 0, and it repeats fully after 400 years.

Is calendar reasoning asked in SSC exams?

Yes. Calendar questions are asked in SSC CGL, CHSL and MTS reasoning, but the number changes from year to year.

How much time should I take for a calendar question?

About 40 seconds after practice.

What are the common mistakes?

Counting a century year as a leap year without checking 400, and forgetting the odd days of the given date.