Calendar

Calendar, Mental Ability Test (MAT)

Definition

A calendar is a system of organizing days for special, religious, commercial, or administrative purposes. This is done by giving names to periods of time, typically days, weeks, months, and years.

Basic Concepts of Calendar

There are some basic concepts of calendar which are as follows : -

Leap Year : -

A Leap year has 366 days. In a leap year, the month of February has 29 days. Every year divisible by 4 is a leap year, if it is not a century.

Example : -
1996, 2004, 2008 etc. are leap years.
1991, 1999 are not leap years.

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

Counting of Odd days : -

  • 1 ordinary year = 365 days = (52 weeks + 1 day)
  • 1 ordinary year has 1 odd day.
  • 1 leap year = 366 days = (52 weeks + 2 days)
  • 1 leap year has 2 odd days.
  • 100 years = 76 ordinary years + 24 leap years
    = $(76 \times 1 + 24 \times 2)$ odd days = 124 odd days.
    = (17 weeks + 5 odd days)
  • Number of odd days in 100 years = 5
  • Number of odd days in 200 years = $(5 \times 2) = 3$ odd days.
  • Number of odd days in 300 years = $(5 \times 3) = 1$ odd day.
  • Number of odd days in 400 years = $(5 \times 4) = 0$ odd day.

    Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc has 0 odd days. As First January 1 AD was Monday. we must count days from Sunday i.e., Sunday for 0 odd day,Monday for 1 odd day,Tuesday for 2 odd day and so on. Last day of a century can not be either Tuesday or Thursday or Saturday. The first day of a century must either be Monday or Tuesday or thursday or saturday.

Example : -
9 December 2001 is Sunday.What was the day on 9 December 1971 ?
Solution : - Total numbre of days = 30 x 365 +8 days from leap years = 10958
When 10958 devided by 7, it have 3 odd days.
so sunday + 3 odd days = Thursday

Calendar Exercise