**Calenders**

Important Facts and Formulae:

**
a) Odd Days :** The number of days more than the complete number of weeks in a given period is number of odd days during that period.

**b) Leap year :** Every year which is divisible by 4 is called a leap year. Thus each one of he year 1992,1996,2004,2008,..etc, is a leap year.

Every 4th century is a leap year but no other century is a leap year thus each one of 400,800,1200,1600,2000,etc is a leap year. None of the 1900,2010,2020,2100,etc is a leap

year. An year which is not a leap year is called Ordinary year.

c)An ordinary year has 365 days.

d) A leap year has 366 days.

e)Counting of odd days :

i)1 ordinary year = 365 days =52 weeks+1 day,Therefore An

ordinary year has 1 Odd day.

ii)One leap year = 366 days =52 weeks+2 days, Therefore a leap

year has 2 Odd days.

iii) 100 years = 76 ordinary years+ 24 leap years

= [(76*52) weeks+76 days]+[(24*52)weeks+48 days]

= 5200 weeks+124days=[5217 weeks+5 days]

therefore 100 years contain 5 odd days

iv)200 years contain 10(1week+3days), i.e 3 odd days

v)300 years contain 15(2 weeks+1 day), i.e 1 odd day

vi)400 years contain (20+1), i.e 3 weeks,so 0 Odd days

similarly each one of 800,1200,1600,etc contains 0 odd days.

Note:(7n+m) odd days , where m less than or equal to 7

is equivalent to m odd days ,thus ,8 odd days = 1 odd day etc.

f) Some codes o remember the months and weeks:

a) Week

Sunday – 1

Monday – 2

Tuesday – 3

Wednesday – 4

Thursday – 5

Friday – 6

Saturday – 0

b) Month

jan – 1 july – 0

feb – 4 Aug – 3

Mar – 4 Sep – 6

Apr – 0 Oct – 1

May – 2 Nov – 4

june – 5 Dec – 6

**Simple problems:**

Shortcuts : This shortcut must be applied only starting

with 19 series.

Example:

**What day of the week on 17th june , 1998? **

Solution : 5 -> the given month code(august)

17 -> the given date

98->(19 th century after years)

24-> ((47/4) = 11 i.e how many leap years

——–

total = 144 ((144/7) = 20 and the remainder is 4)

therefore in the above week table the no 4 code

represents wednesday

so the required day is wednesday.

**Problem 1:**

**The first republic day of the India was celebrated on 26th January,1950. It was **

Solution : 01

26

50

12

———-

total = 89 ((89/7) = 12 and the remainder is 5)

therefore in the above week table represents the number 5

as thursday, so the required day was Thursday.

**Problem 2:
Find on which day 15th august1947 ? **

Solution :

03

15

47

11

———-

total = 76

Then (76)/7 = 6 odd days

6 indicates friday in the above week table.

Therefore required day is friday.

**Problem 3:
Find on which day jan 26th 1956 ? **

Solution :

01

26

56

14

-1 (-1 indicates leapyear(i.e 1956),so 1 reduce from the total)

———

total = 96

Then (96)/7 = 5 odd days

5 indicates thursday in the above week table

Therefore our required day is Thursday.

Problem 4:

Today is friday after 62 days,it will be :

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

so, after 63 days,it will be friday. Hence ,after 62 days,

it will be thursday.

Therefore the required day is thursday.

**Problem 5:
Find the day of the week on 25th december,1995? **

Solution :

06

25

95

23

———

total = 149

Then (149)/7=(23)=2 odd days

Therefore the required day is “Monday”.

**Medium Problems**

Problem 1:

jan 1, 1995 was a sunday.what day of the week lies on jan 1,1996?

Solution :

01

01

96

24

-1(since 1996 was leap year)

———

total = 121

Then (121)/7 = (17) = 2 odd days

Therefore our required day wasMonday.

Problem 2:

On 8th feb,1995 it wednesday. The day of the week on 8th feb,1994 was?

Solution :

04

08

94

23

———

total = 129

Then (129)/7 = (18) = 3 odd days

Therefore the required day is Tuesday.

**Problem 3:
may 6,1993 was thursday.what day of the week was on may 6,1992 ? **

Solution :

02

06

92

23

-1

———-

total = 122

Then (122)/7 = (17) = 3 odd days

Therefore the required day is Tuesday

**Problem 4:
jan 1, 1992 was wednesday. What day of the week was on jan 1,1993 ? **

Solution :

01

01

93

23

———-

total = 118

Then (118)/7 = (16) = 6 odd days

Therefore the required day is Friday.

Problem 5:

January 1,2004 was a thursday,what day of the week lies on jan ,2005?

solution :

The year 2004 being a leap year, it has 2 odd days. so,

first day of the 2005 will be 2 days beyond thursday and

so it will be saturday

therefore the required day is Thursday.

**Problem 6:
On 8th march,2005,wednesday falls what day of the week was it on 8th march,2004?**

Solution : the year 2004 being a leap year,it has 2 odd days.

so, the day on8th march,2005 will be two days beyond the day

on 8th march,2004.but 8th march,2005 is wednesday. so,

8th march,2004 is monday.

Therefore the required day is Monday.

Problem 7:

what was the day of the week on 19th september ,1986 ?

Solution :

06

19

86

21

———

total = 132

Then ((132/7 = 18 and the remainder is 6)

In the above week table represents the number 6 is friday.

Therefore the required day is Friday.

**Typical problems**

**Problem 1:
On what dates of october,1994 did monday fall ?
**

Solution : 01

01

94

23

——-

total = 119

Then (119)/7 = (17) = 0 odd days

so the day is saturday

Therefore in october first the day is saturday.so,

the monday fell on 3rd october 1994.During october 1994,

monday fell on 3rd ,10th,17th and 24th.

**Problem 2:
How many days are there from 2nd january 1995 to 15 th march,1995 ?**

Solution : Jan + Feb + March

30 + 28 + 15 = 73 days

**Problem 3:
The year next to 1996 having the same calendar as that of 1996 is ?**

Solution : Starting with 1996 , we go on countig the

number of odd days till the sum is divisible by 7.

Year 1996 1997 1998 1999 2000

odd days 2 1 1 1 2

2 + 1 + 1 + 1 + 2 = 7 odd days i.e odd day.

Therefore calendar for 2001 will be the same as

that of 1995.

**Problem 4:
The calendar for 1990 is same as for :**

Solution:

count the number of days 1990 onwards to get

0 odd day.

Year 1990 1991 1992 1993 1994 1995

oddd days 1 1 2 1 1 1

1 + 1 + 2 + 1 + 1 + 1 = 7 or 0 odd days

Therefore calendar for 1990 is the same as for the

year 1996.

Problem 5:

The day on 5th march of year is the same day on what date of the same year?

Solution:

In the given monthly code table represents the march code and november code both are same.that means any date in march is the same day of week as the corresponding date in november of that year, so the same day falls on 5th november.

hai

Very very thank you for ur work, sir..

your work for fresher is too good thank you very much.

what is the day on 31st oct 1984?how

hey.. great material..

hey.. ur solution for problem no 4 is wrong.. the calendar for 1990 and 1996 are not the same..

great it helps us in many exms thnku very much

excellent.!! thank u very much

hey….. ur sln for pblm no 4 is wrong.the calender for 1990 and 1996 r not the same

hai

Ok this is very helpfull for copmtative exam.

Regards

radhey shyam

9560693583

kevalam

yenaku nenga fan thana

I didnt understand the 4th line

there is no same calender 1990 1996

1996 and 2001

1995 and 2001

all you are cheater

copy question from R.S Agrawal and paste here

lund mera kuch nahi hoga isase

odd days assigning number rong.so change the assigning value

Could anyone tell me in problem1 no.12 how will come.

thanks

hello frdz, 100 years=76 ordinary yrs + 24 leap yrs.how it happened?plz someone make me clear.

hi frndz,in ur shortcut method,17 june 1998

24=47/7=11 i.e how many leap year.plz give explanation of 24.plz ans fast as soon as possible.