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Chapter - 20


Ordinary year: An year having 365 days is called an ordinary years.

Leap year: Year having 366 days is called a leap year. Every leap year is exactly divisible by 4 and ordinary years are not completely divisible by 4.

Calculation of leap yearCalculation of leap year

Odd  days: In a given period, the days apart from complete weeks are called odd days. An ordinary year has one odd day i.e. 365/7 = 52 weeks + 1 days

While the leap year has two odd days i.e. 366/7 = 52 + 2 days

To find the number of odd days.

In 100 years there are 24 leap years + 76 ordinary years

= 24 x 52 weeks + 24 x 2 days + 76 x 52 weeks + 76 days

= 6 days  + 6 days

= 12 days = 1 week and 5 days

so in 100 years there are 5 odd days

similarly in 200 years there are 3 odd days

and in 300 years there are 1 odd day

in 400 years there is 0 odd day

similarly in 800 years, 1200 years and 1600 years there is 0 odd day

odd days in Feb: In an ordinary year Feb has no odd day, where as in a leap year Feb has one odd day.

1st day of the century must be Tuesday, Thursday or Saturday and Last day of a century cannot be Tuesday, Thursday or Saturday.

To find a particular day when a

Day and a date is given.

Step 1: Find out the number of odd days between the given date and the date for which the day is to be found one.

Step II: From the given day count the odd days in the forward direction to arrive at the day on the given date.

Example: If 10th January 1992 was Saturday, what day of the week was on 6th March, 1993.

Solution: Calculate number of odd days between 10th Jan 1992 and 6th Mar 1993

Jan 10, 1992 is Saturday

So from Jan 11 to Dec 31 of 1992 – days are 366 – 10

= 356 days

Jan 1993                       = 31days

Feb 1993                       = 28 days

6th March 1993               = 6 days

Total days =                  = 421

= 60 weeks + 1 day

So No. of odd days = 1

Let us count one day after Saturday

The required day will be Sunday.

Example 2: on April 4, 1988 it was Monday. What day of the week was on 5th Nov. 1987.

Solutions: No. of days between 5th Nov. 1987 to 4th April 1988

6th Nov 1987 to 30 Nov  = 25 days

Dec 1987                       = 31 days

Jan 1988                                   = 31 days

Feb 1988                       = 29 days

March 1988                    = 31 days

4th April 1988                  = 4 days

Total     = 151 days

No. of odd days = 151 / 7 = 21 weeks – 4 days

So since 5th Nov. 1987 is prior to 4th April 1988

We are to cannot 4 days backwards from Monday

Requried day is Thursday

To find the day on a particular date if day and date is not given.

The procedure can be understood from the given example.

Example 3: Find the day of the week on 26th Jan. 1960.

Solution: No. of odd days upto 26th Jan. 1960

= Odd days for 1600 years + odd days for 300 years

+ odd days for 59 years + odd days of 26 days of Jan 1960

= 0 + 1 + 59 + 14 + 5 = 79 days

= 79 / 7 = 11 weeks + 2 days = 2 odd days

The required day is Tuesday

Zero odd day means Sunday. We are to consider one odd day as Monday

2 odd days as Tuesday and so on

The document Calendar | Quantitative Techniques for CLAT is a part of the CLAT Course Quantitative Techniques for CLAT.
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FAQs on Calendar - Quantitative Techniques for CLAT

1. What is a calendar?
Ans. A calendar is a system used to organize and measure time, typically divided into days, weeks, months, and years. It helps in keeping track of important dates, events, holidays, and scheduling activities.
2. How does a calendar work?
Ans. A calendar works by mapping the progression of time using a specific system. It typically follows the Earth's revolutions around the sun, which determines the length of a year. Days are divided into hours, hours into minutes, and minutes into seconds, providing a way to measure time intervals accurately.
3. What are the different types of calendars?
Ans. There are various types of calendars used worldwide, including the Gregorian calendar (the most widely used), the Islamic calendar, the Chinese calendar, the Hindu calendar, and many more. Each calendar system may have its own unique way of determining dates and organizing time.
4. How does the Gregorian calendar differ from other calendars?
Ans. The Gregorian calendar is a solar calendar introduced by Pope Gregory XIII in 1582. It is based on the Earth's revolution around the sun and consists of 365 days in a year, with an additional leap day added every four years. It is widely used internationally and has become the standard calendar for most countries.
5. Are there any significant events associated with calendars?
Ans. Yes, calendars often mark significant events, holidays, and observances. Some examples include New Year's Day, Christmas, Easter, Independence Day, religious festivals, national holidays, and cultural celebrations. Calendars also help in scheduling important events such as meetings, appointments, and deadlines.
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