Aptitude - Calendar - Discussion

You are right, thanks @Sri Harsha.

The output of = years (date (2016, 5, 1), date (2013, 5, 1), 0) will return.

Could anyone explain me why are we considering 300 years? .

For those who did not understand this problem,let me try to explain you.

The first thing to be cleared is that for every 400 years there are 0 odd days.

This is because,in 400 years,there are 97 leap years and 303 ordinary years(remember that 100,200,300 are not leap years but 400 is a leap year.Because any year ending with 00,that year should be divisible by 400 in order to become a leap year)

So the number of odd days at the end of 400 years will be [(97*2)+(303*1)]=497 days.Convert this into weeks,we get 71weeks + 0odd days=totally 0 odd days

Now coming to the problem,
1997=1600+397
for 1600 years 0 odd days
therefore 397 years can be classified as
1601-1700-->24 leap years + 76 ordinary years=[(24*2)+(76*1)]=
124 odd days
1701-1800-->24 leap years + 76 ordinary years=124 odd days
1801-1900-->24 leap years + 76 ordinary years=124 odd days
1901-1997-->24 leap years + 73 ordinary years=121 odd days
totally we have 124*3 + 121=493 odd days
convert this into weeks=70weeks +3 odd days
Hence at the end of the year 1997,we have 3 odd days

Now coming to the year 1998,
the number of odd days=31+28+31+30+31+17=168 odd days(jan,feb,...jun17th)
Convert this into weeks=24weeks +0 odd days
Hence the total odd days=3+0=3 odd days
therefore 17th june 1998=Wednesday

We can calculate the day of week based on current date and day.

Whenever we got back one year on the same date the day of week will be one less than today's day of week.

For example today is 27th january 2014 Monday means 27th january 2013 was one day behind of Monday i.e Sunday.

If the year is leap year the day of week goes back 2 days for examples if 27th january 2013 is Sunday and the previous year 2012 is leap year so 27th january 2012 will be two day behind sunday i.e friday. If like this we calculate we have :

27th january 2013 - Sunday.
2012 - Friday 2011 - thur 2010 - wed 2009 - tue 2008 - sun.
2007 - sat 2006 - fri 2005 - thur 2004 - tue 2003 - mon .
2002 - sun 2001 - sat 2000 - thur 1999 - wed 1998 - tues.

SO now 27th January 1998 was tuesday.
To calculate : 17th june 1998 what day?

Jan Feb Mar Apr May june
5 days 28days 31d 30d 31d 17d Total = 142d
(31-27
including 27)

Now total = 142 days between 27th january 1998(Tuesday) and 17th june 1998 .

To calculate the day divide total no of days by 7 and check the remainder. If remainder is 0 it would be previous day of week. If remainder is 1 it would be same day of week. If remainder 2 it would be next day of week and so on.

So here 142/7 = 20 and remainder 2 so the day of week would be Wednesday(Next day of Tuesday).

Thank you @Arya, @Inshan, @Nitesh.

Why we took 300 years?

How to calculate odd days for 300 years?

499*2=899 = no of odd day in leap(for understand)
1996-499=1497 odd day in remaining year (for understand)
odd day 899+1497= 2396 total odd day (for understand)
2396/7= 342+ 2/7=> 2odd day (actual odd day till 1996)
2+1= 3 odd day till 1997 (actual odd day till 1997)
then 1 Jan 1998= thursday
Jan 31
Feb 28
mar 31
april 30
may 31
june 17= wedenesday

@Hi Shruthi,.

It is measured that each 100year has 5 odd days OK ?.

(remember it always don't ask why because this is not our main problem).

So, for 300years 5*3=15 odd days.

But 15 days are convert-able in weeks.

So, 15/7 = 2 weeks + 1 odd days.

(leave days for week, now they are not odd).

That's why 300years = 1 odd day.