Slide 1 : www.mitochondria.asia presents Dates and Days
Lets learn to find corresponding days on given dates
Objective : Objective Now a days rarely any competitive exam’s preparation is complete without learning techniques to find the day on a given date. Here is a small yet fun learning exercise for all of us who are new to questions related to dates and days.
1. Terms : 1. Terms Lets start with learning few terms which will be useful to us at a later stage, in case we aren’t already familiar with them. For experts please jump to slide 8, as time is a precious commodity and we respect our time.
Ordinary year
Leap Year
Odd day
1.1 Ordinary year : 1.1 Ordinary year Any year which has 365 days is known as ordinary year. It has 12 months each having a particular number of days as given in the table below. Also it has 52 weeks with a day to spare.
Number of days for each month are given below in the table.
1.2 Leap Year : 1.2 Leap Year Any year which has 366 days is known as Leap year. It also has 12 months each having a particular number of days as given in the table below. It also it has 52 weeks but with two day to spare. The extra day come from February which has 29 days in a leap year.
How to know it’s a ordinary year or a Leap year. : How to know it’s a ordinary year or a Leap year. Its easy! Just divide the last two digits of year by 4, if we don’t get any remainder it’s a Leap year otherwise its not.
Lets see some examples.
Q. Is 2004 a leap year?
S. As we have learned earlier, we divide last two digits (04) by 4 and find that there is no remainder so it’s a leap year.
How to know it’s a ordinary year or a Leap year. : How to know it’s a ordinary year or a Leap year. Q. Is 1886 a leap year?
A. Certainly not! 86 is not divisible by 4 completely. ( It leaves a remainder of 2).
Now lets see if year 1000 was leap year. Here last two digits are 00, so how do we find out if year 1000 is a leap year? Well not so difficult, in case of any century take first two digits instead of last two. Its easy again! First two digits 10 is not divisible by 4 completely so… not a leap year.
1.3 Odd Days. : 1.3 Odd Days. Odd day is the most useful day while we will calculate the day for any given date, as we’ll come to know later.
Well what is this Odd Day? Do we remember that one spare day in a ordinary year or two in a leap year, yes that is our odd day.
By Definition number of days left after dividing any number of days by a week (that is 7 days) are odd days.
Calculation of odd days. : Calculation of odd days. Now we know what are odd days, its easy.
In a ordinary year we have 1 odd day.
In two ordinary years we have 2 odd days.
In a three consecutive years having a leap year in between we have 4 odd days. (why?)
Calculation of odd days. : Calculation of odd days. In January we have 3 odd days.
In a February of a ordinary year we don’t get any odd day.
From March to December any year we’ll have 4 odd days. ( Why? Total spare days are 25, exceeding a week (7 days) so again dividing by 7, we get 4 odd days)
Calculation of odd days. : Calculation of odd days. Lets see how many odd days we have in a 100 years.
First we need to know how many leap and ordinary years we have here.
Here leap years would be 24 (why? Because usually a starting year of a century is not a leap year, only 400,800,1200,1600,2000 are leap years, again why? It’s a easy one).
So, ordinary years, 76 (=100-24).
No of spare days = 76x1 + 24x2 =124 spare days =17 weeks + 5 odd days.
Calculation of odd days. : Calculation of odd days. Lets see how many odd days are there in 200 years.
Easy! 3 Odd days.
In 100 years 5 Odd Days. So in 200 years 10 spare days = 3 Odd days ( = 10 -7 )
Calculation of odd days. : Calculation of odd days. Similarly how many odd days are there in 300 years.
Yes! It is indeed 1 odd day.
Calculation of odd days. : Calculation of odd days. How about number of odd days in 400 years.
What 6 odd days?
No dear its 0 odd days.
How? Lets calculate.
In 400 years, we have 97 Leap years and 303 ordinary years, leaving us with 497 spare days (=97x2+303), leaving no odd days.
Ok, why 97 leap years and not 96(=24+24+24+24), because every 400 years at least one century ends with a leap year. (Why?)
2. Odd days and day. : 2. Odd days and day. Now we need to learn a simple table in order to find out day on a given date. Here it is.
1.3 Lets do some examples : 1.3 Lets do some examples Example 1: On what day India got Independence?
Answer: Friday. If we are good at General Knowledge.
For those who are like me, lets find out how we do this.
Solution: We were declared Independent on August 15, 1947. If we can find how many odd days we have till August 15, 1947, we’ll have our answer.
Solution Contd… : Solution Contd… Lets calculate.
Till 1600 we have 0 odd days.
Number of odd days in next 300 years = 1
From 1901-1946: 11 Leap years + 35 Ordinary years.
Spare days : 11x2+35x1=57 days.
That is; 57 days = 8 weeks + 1 odd days.
From Jan to Aug 15 no of spare days = 17
That is; 17 days = 2 weeks + 3 odd days.
Total Odd days = 5, which corresponds to Friday. Wow! We got the answer in spite of not being good at GK.
1.4 Lets do some more… : 1.4 Lets do some more… Q1. On what day Father of our nation was assassinated?
Q2. What day I was born, given that I was born on 21 October 1979.
A1. Friday.
A2. Sunday.
1.5 Summary : 1.5 Summary Odd days in a year = 1
Odd days in a leap year = 2
Odd days in 100 years = 5
Odd days in 200 years = 3
Odd days in 300 years = 1
Odd days in 400 years = 0
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