A calendar helps us organize days, weeks, and months in a proper order so that we can easily find any date, month, or day of the week. In reasoning questions based on calendars, you may be asked to find the day of the week for a given date, either with or without a reference date. Sometimes, you may have to find one weekday based on another.
UPSC Exam > UPSC Notes > CSAT Preparation > Basic Concepts: Calendars
Basic Concepts: Calendars | CSAT Preparation - UPSC PDF Download
| Table of contents |
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| What is a Calendar? |
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| Types of Calendar Reasoning Questions |
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| Tips and Tricks for Calendar Questions |
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| Solved Examples |
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We all use calendars in our daily lives, but have you ever wondered which calendar is the most widely used in the world? It’s the Gregorian Calendar, which is also recognized as the National Calendar of India, adopted on 22nd March, 1957.
In the context of competitive exams, calendar reasoning is a frequently tested topic. Exams such as UPSC, SSC, RBI Grade B, SBI PO/Clerk, IBPS PO/Clerk, and others often include questions from this section. These questions are typically straightforward and easy to solve, making them great for scoring.
To answer calendar reasoning questions accurately, it is important to carefully read the question and understand what is being asked before attempting a solution. Having a strong grasp of the basic concepts and question types related to calendars can significantly improve your performance in this section.
What is a Calendar?
Before diving into solving such problems, it's essential to understand some basic calendar concepts.
Basic Concepts to Remember
- Day: The smallest unit of a calendar. One day equals 24 hours and is 1/7th of a week.
- Week: A group of 7 consecutive days — Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday. A week is 1/52nd of a year.
- Month: A month has 28, 29, 30, or 31 days and is 1/12th of a year.
- Year: The time the Earth takes to complete one revolution around the Sun. A year is 1/100th of a century.
- Date: A specific day marked on the calendar. It is 1/28th, 1/29th, 1/30th, or 1/31st of a month, and 1/365th or 1/366th of a year.
- Century: A span of 100 years.
- Ordinary Year: Has 365 days, which is equal to 52 weeks and 1 odd day. Ordinary years are not divisible by 4.
- Leap Year: Has 366 days, i.e., 52 weeks and 2 odd days. A year is a leap year if it is divisible by 4. However, century years must be divisible by 400 to qualify as leap years.
- Example: 1900 is not a leap year (not divisible by 400)
- Example: 2000 is a leap year (divisible by 400)
Types of Calendar Reasoning Questions
Now that we know what calendar reasoning is, let’s look at the different types of questions that are asked in this section:
1. Counting Odd Days
In these questions, you are asked to find how many extra days are left after forming complete weeks. These extra days are called odd days.
To find the number of odd days, divide the total number of days by 7. The remainder gives you the odd days.
Example: How many odd days are there in 1000 years?
Solution:
1000 – 800 = 200 (We subtract the nearest multiple of 100)
In 100 years, there are 5 odd days. So in 200 years, there will be 10 odd days.
2. With Reference Date
Here, a known day and date is given. You have to find the day on another date using this information.
Example: If today is Monday, what day will it be after 128 days?
Solution:
128 days = 18 full weeks (126 days) + 2 days = 2 odd days
So, after Monday, the day will be Wednesday.
3. Without Reference Date
In these questions, a specific date is given but no day is provided. You have to calculate the day from scratch.
Example: What was the day on 26th January 1950?
Solution (in brief):
1600 years = 0 odd days
300 years = 1 odd day
49 years = 12 leap years + 37 normal years = 12×2 + 37 = 61 = 5 odd days
Add 26 days of January = 5 odd days
Total = 0 + 1 + 5 + 5 = 11 → 4 odd days
So, the day was Thursday.
4. Repetition
These questions ask you to find another year or month that will have the same calendar as the one given.
Example: Which year will have the same calendar as 2001?
Solution:
We add the number of odd days for each year until the total is 7 (or a multiple of 7).
Odd days from 2002 to 2007 = 1 + 1 + 1 + 2 + 1 + 1 = 7
So, 2007 has the same calendar as 2001.
Tips and Tricks for Calendar Questions
Below are some practical tips and tricks to help you solve calendar reasoning questions effectively in competitive exams:
Tip 1: In an ordinary year, the first day of the month is the same for these pairs or groups of months: January and October, April and July, February-March-November, September and December.
Tip 2: In a leap year, the first day of the month is the same for: January-April-July, February and August, March and November, September and December.
Tip 3: The first day of any century year (like 1700, 1800, 1900, etc.) is always a Monday, Wednesday, Friday, or Saturday. The last day of a century year is never Tuesday, Thursday, or Saturday.
Tip 4: A calendar will repeat in another year only when the total number of odd days between the two years is zero.
Tip 5: A leap year calendar repeats after 28 years, while the calendar of an ordinary year repeats after 6 or 11 years. This can help you eliminate options quickly without checking all of them.
Tip 6: Odd days in centuries follow a fixed pattern:
100 years = 5 odd days
200 years = 3 odd days
300 years = 1 odd day
400 years = 0 odd days
Knowing these fixed values helps in faster calculation of the day of the week for any date.
Solved Examples
Example 1: Today is Wednesday. After 45 days, what day will it be?
Solution:
Solution:
- 45 ÷ 7 = 6 weeks + 3 days.
- Wednesday + 3 days = Saturday.
Answer: Saturday.
Example 2: If July 12, 2010, is a Monday, what was the day on July 12, 2009?
Solution:
- 2009 is not a leap year (365 days = 1 odd day).
- July 12, 2010 (Monday) - 1 day = July 12, 2009.
- Monday - 1 day = Sunday.
Answer: Sunday.
Example 3: If December 25, 1990, is a Tuesday, what day is December 25, 2020?
Solution:
Calculate odd days from 1990 to 2020: 38 odd days (1+1+2+1+1+1+2+1+1+1+2+1+1+1+2+1+1+1+2+1+1+1+2+1+1+1+2+1+1+1+1) = 3 odd days.
- Tuesday + 3 days = Friday.
Answer: Friday.
Example 4: What is the day on April 15, 2079?
Solution:
- From year 2000: 78 years = 19 leap years (38 odd days) + 59 normal years (59 odd days) = 97 odd days = 6 odd days.
- From January 1 to April 15: 31+28+31+15 = 105 days = 0 odd days.
- Total odd days = 6. January 1, 2079, is 6 days from Sunday = Saturday.
- April 15, 2079, is Saturday (same as January 1).
Answer: Saturday.
Example 5: If February 2, 2012, was a Wednesday, when will it repeat?
Solution:
- 2012 is a leap year; its calendar repeats every 28 years.
- 2012 + 28 = 2040.
Answer: 2040.
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FAQs on Basic Concepts: Calendars - CSAT Preparation - UPSC
| 1. What is a calendar? |  |
Ans. A calendar is a system that helps organize and track time, typically based on the cycles of the sun and the moon. It consists of a series of months, weeks, and days, allowing us to plan and schedule events.
| 2. How are calendars used in our daily lives? | |
Ans. Calendars are used in our daily lives for various purposes. They help us keep track of important dates such as birthdays, anniversaries, and holidays. Calendars also assist in planning and managing appointments, meetings, and deadlines.
| 3. What are the different types of calendars? | |
Ans. There are several types of calendars used worldwide. Some common ones include the Gregorian calendar, which is widely used internationally, and the lunar calendar, based on the moon's cycles. Other types include solar calendars, lunisolar calendars, and various cultural or religious calendars.
| 4. How does the Gregorian calendar work? | |
Ans. The Gregorian calendar, named after Pope Gregory XIII, is a solar calendar widely used around the world. It consists of 365 days in a year, divided into 12 months. Leap years, occurring every four years, have an extra day in February (29 days instead of 28) to account for the discrepancy between the solar year and the calendar year.
| 5. Can calendars be personalized or customized? | |
Ans. Yes, calendars can be personalized or customized according to individual preferences. Many digital calendars and apps allow users to add their own events, reminders, and color-coding options. Additionally, there are services that offer customizable printed calendars, allowing you to include personal photos or artwork.
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