1) What was the day of the week on 15th august 1947 ?
Solution : 15th August 1947=(1946 Years + period from jan1st 1947 to August 15th 1947)
2) What was the day of the week on 16th April 2000 ?
Solution : 16th April 2000=(1900 Years +99 Years+ period from jan1st 2000 to 16th April 2000)
Caliculating odd days for 1900 years : 1600 + 300 years =0+1=1 odd day
Caliculating odd days for 99 years : (24 Leap years +75 ord years)=(24*2+75*1)=123 odd days=4 odd days (since 123/7 reminder is 4)
Caliculating odd days for period from jan1st 2000 to 16th April 2000 :
Jan+Feb+Mar+April(Upto 16th)=31+29+31+16 =107 days =2 odd days (since 107/7 reminder is 2)
Therefore total odd days =1+4+2=7 =0 odd days (7/7 reminder 0)
Hence the the day of the week on 16th April 2000 is Sunday
3) On What days of july 2004 did Monday fall?
Solution :First We will find what is the day on 1st July 2004
1st jan 2004 =(2000years+3 years + period from jan1st 2004 to 1st July 2004)
=(0+3+(jan+feb+ mar+Apr+may+june +1 day in july)
=(3+31+29+31+30+31+30+1)=186 days =4 odd Day (186/7then 4 reminder)
Hence 1st July 2004 was Thrusday.
Hence 1st Monday in july 2004 was on 5th july 2004.
Hence during july Monday will fell on 5th,12th,19th,26th
4) For 2003 calender which of the calendar has same calendar
a) 2014 b) 2015 c)2018 d)2022
First caliculate the odd days between from 2003 to 2014 : 14 (please exclude 2003 and 2014) .As it is a multiple of 7 hence both have the same calendar.
simillarly caliculate the odd days between from 2003 to 2015 : 15 (please exclude 2003 and 2015) .As it is not a multiple of 7 hence both does not have the same calendar.
Solution : 15th August 1947=(1946 Years + period from jan1st 1947 to August 15th 1947)
Caliculating odd days for 1946 years :
1946 Years =1600+300+(11 leapyears+ 36 rd.years)=0+1+(11*2+36*1) odd days
=1+48=49 odddays=3 odd days (59/7 –Reminder is 3)
Caliculating odd days for period from jan1st 1947 to August 15th 1947:
Jan+Feb+mar+Apr+may+Jun+july+Aug=31+28+31+30+31+30+31+(15 days in august)
=227 days
=3 odd days
Therefore total odd days =3+3 =6
The 6th day is Saturday
Hence the day of the week on 15th august 1947 is Saturday
1946 Years =1600+300+(11 leapyears+ 36 rd.years)=0+1+(11*2+36*1) odd days
=1+48=49 odddays=3 odd days (59/7 –Reminder is 3)
Caliculating odd days for period from jan1st 1947 to August 15th 1947:
Jan+Feb+mar+Apr+may+Jun+july+Aug=31+28+31+30+31+30+31+(15 days in august)
=227 days
=3 odd days
Therefore total odd days =3+3 =6
The 6th day is Saturday
Hence the day of the week on 15th august 1947 is Saturday
2) What was the day of the week on 16th April 2000 ?
Solution : 16th April 2000=(1900 Years +99 Years+ period from jan1st 2000 to 16th April 2000)
Caliculating odd days for 1900 years : 1600 + 300 years =0+1=1 odd day
Caliculating odd days for 99 years : (24 Leap years +75 ord years)=(24*2+75*1)=123 odd days=4 odd days (since 123/7 reminder is 4)
Caliculating odd days for period from jan1st 2000 to 16th April 2000 :
Jan+Feb+Mar+April(Upto 16th)=31+29+31+16 =107 days =2 odd days (since 107/7 reminder is 2)
Therefore total odd days =1+4+2=7 =0 odd days (7/7 reminder 0)
Hence the the day of the week on 16th April 2000 is Sunday
3) On What days of july 2004 did Monday fall?
Solution :First We will find what is the day on 1st July 2004
1st jan 2004 =(2000years+3 years + period from jan1st 2004 to 1st July 2004)
=(0+3+(jan+feb+ mar+Apr+may+june +1 day in july)
=(3+31+29+31+30+31+30+1)=186 days =4 odd Day (186/7then 4 reminder)
Hence 1st July 2004 was Thrusday.
Hence 1st Monday in july 2004 was on 5th july 2004.
Hence during july Monday will fell on 5th,12th,19th,26th
4) For 2003 calender which of the calendar has same calendar
a) 2014 b) 2015 c)2018 d)2022
First caliculate the odd days between from 2003 to 2014 : 14 (please exclude 2003 and 2014) .As it is a multiple of 7 hence both have the same calendar.
Year | odd days |
2004 | 2 |
2005 | 1 |
2006 | 2 |
2007 | 1 |
2008 | 2 |
2009 | 1 |
2010 | 1 |
2011 | 1 |
2012 | 2 |
2013 | 1 |
simillarly caliculate the odd days between from 2003 to 2015 : 15 (please exclude 2003 and 2015) .As it is not a multiple of 7 hence both does not have the same calendar.
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