CALENDAR : calendar is used to find many problems related to odd days, leap year, and counting of odd days and many.

**Condition for Calender :
1. Odd Days: **We are supposed to find the day of the week on a given date. For this, we use the concept of

**'odd days'.**

**or**

In a given period, the number of days more than the complete weeks are called

**odd days.**

**2. Leap Year:**

**(a).** Every year divisible by 4 is a leap year, if it is not a century.

**(b).** Every 4th century is a leap year and no other century is a leap year.

Note: A leap year has 366 days.

**Examples:**

**(a)** Each of the years 1948, 2004, 1676 etc. is a leap year.

**(b)** Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.

**(c)** None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.

**3.Ordinary Year:**

The year which is not a leap year is called an ordinary years. An ordinary year has 365 days

**Counting of Odd Days:**

**1**. 1 ordinary year = 365 days = (52 weeks + 1 day.) 1 ordinary year has 1 odd day.

**2. **1 leap year = 366 days = (52 weeks + 2 days) 1 leap year has 2 odd days.

**3 . **100 years = 76 ordinary years + 24 leap years

= (76 x 1 + 24 x 2) odd days = 124 odd days.

= (17 weeks + days) = 5 odd days.

Number of odd days in 100 years = 5

Number of odd days in 200 years = (5 x 2) 3 odd days.

Number of odd days in 300 years = (5 x 3) 1 odd day.

Number of odd days in 400 years = (5 x 4 + 1) 0 odd day.

Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days

## Calendar Important Examples and Formulas

**Question-1: **It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

**Solution: **On 31st December, 2005 it was Saturday.

Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.

On 31st December 2009, it was Thursday.

Thus, on 1st Jan, 2010 it is Friday.

**Question-2: **What was the day of the week on 28th May, 2006?

**Solution : **28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)

Odd days in 1600 years = 0

Odd days in 400 years = 0

5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days

Jan. Feb. March. April. May

(31 + 28 + 31 + 30 + 28 ) = 148 days

148 days = (21 weeks + 1 day) 1 odd day.

Total number of odd days = (0 + 0 + 6 + 1) = 7 0 odd day. Given day is Sunday.

**Question-3 : **On what dates of April, 2001 did Wednesday fall?

**Solution : **We shall find the day on 1st April, 2001.

1st April, 2001 = (2000 years + Period from 1.1.2001 to 1.4.2001)

Odd days in 1600 years = 0

Odd days in 400 years = 0

Jan. Feb. March April

(31 + 28 + 31 + 1) = 91 days 0 odd days.

Total number of odd days = (0 + 0 + 0) = 0

On 1st April, 2001 it was Sunday. In April, 2001 Wednesday falls on 4th, 11th, 18th and 25th.

**Question-4 : **Today is Monday. After 61 days, it will be:

**Solution : **Each day of the week is repeated after 7 days.

So, after 63 days, it will be Monday. After 61 days, it will be Saturday

## Calendar Important Questions from Previous Year Exams

Calender Aptitude

## Calender Important Video

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