# Introduction

Article prepared with help of Mr. Deepak Singh.

There are two main types of questions from Calendar

 when youโre given a reference day when youโre given no reference โDayโ What day of week was it on 5th November, 1989 if it was Monday on 4th April, 1988 ? Monday Tuesday Saturday Sunday What was the day on 15th august 1947? Sunday Monday Tuesday Friday Here question tells us that 4th April 88 was Monday, so we have a โreference โday. Here question doesnโt give us any reference โdayโ. can be solved with just two concepts 7 day cycle โday gain-Day lossโ concept need to just mugup 2 table, and few steps.

Although calendar question is not asked every year in every exam. But If and when calendar question is asked, just follow the given procedure and youโll get the accurate answer= one mark is guaranteed=in that sense, cost: benefit is great.

# Concept: 7 Day cycle

Name of the day will repeat after seven days.

1st August 2013= Thursday. Therefore 1st August + 7 =8th August also has to be Thursday.

Then what day will be 10th August 2013?

1st August =Thursday => 1+7=8 August is also Thursday

And 8 August + 2 =10 August will be Thursday + 2 days =>Saturday.

letโs try a simple question from SSC

# SSC-CGL 2000 Question on 7-Day cycle

If 9th of the month falls on the day preceding Sunday, then on what day will 1st of the month fall?

1. Friday
2. Saturday
3. Sunday
4. Monday

As per the question 9th of the Month=Saturday. (day preceding Sunday)

Day name repeats after 7 days.

Therefore 9 minus 7=2nd of the given month is also Saturday.

Then 1st of the given month= Saturday Minus one day = Friday, Ans A

# Concept: Day Gain Day loss

 +1 year When we proceed forward by one year, then 1 day is gained and vice-versa.Example,9th August 2013 is Friday, therefore 9th August 2014 has to be Friday+1=Saturday.Reverse is also true. When we move backward by one year, then 1 day is lost. 9th August 2014 is Saturday, therefore 9th August 2013 has to be Saturday minus 1=Friday. +2 Leap Year When we proceed forward by one leap year, then 2 days are gained and vice-versa. Example If it is Wednesday on 10th august 2011 โฆ then it would be Friday (Wednesday +2) on 10th august 2012 [because 2012 is a leap year]. The reverse is also correct: If 22nd April, 1988ย  = Friday , then 22nd April,1987 = Wednesday. ย (-2 days)

Exception to Leap Year day gain day lossโ the date must have crossed 28th February if the coming year is a leap year for adding 2 days otherwise add 1 day.

For e.g.

• If 26th January 2011 is Wednesday โฆ then 26th January 2012 would be Thursday (even if 2012 is leap year we have added +1 day, because 28th of February is not crossed).
• If 23rd March 2011 is Wednesday โฆ then 23rd march 2012 would be Friday (+2 days. As 28th February of leap year is crossed).

# What is Leap year?

A normal year has 365 days. A leap year has 366 days (the extra day is the 29th of February)

A year which is divisible by 4 is a leap year except, if it is divisible by 100 then we have to check it by dividing by 400. For e.g.

1. 1988, 2008, 2012, 2016 etc. all are leap years as divided by 4.
2. 2000, 2400, 1600 etc. all are leap as divided by 400 (100 and 4 too).
3. 1700, 1800, 2100, 2200 etc. are not leap years as they are not divisible by 400 (even if they are divisible by 4).

Letโs try a sum

# SSC Investigator 2010 (Anniversary)

On 5th December 1993, Nirmala and Raju celebrated their anniversary on Sunday. What will be the day on their anniversary in 1997?

1. Wednesday
2. Thursday
3. Friday
4. Tuesday

Normal year jump +1 gain; Leap year jump +2 gain.

 years day gain 1994 1 1995 1 1996 (leap year) 2 1997 1 total days 5

Sunday plus five days

1. Monday
2. Tue
3. Wed
4. Thursday
5. Friday

letโs try one more with a bit difference:

# SSC CGL 2011 (Anniversary)

Mrs. Susheela celebrated her wedding anniversary on Tuesday 30th September 1997. What will she celebrate her next wedding anniversary on same day (Tuesday)?

1. 30 Sept 2003
2. 30 Sept 2004
3. 30 Sept 2002
4. 30 October 2003

After 7 days=> day name will repeat

 30th September day gain 1998 1 99 1 2000 (leap) 2 2001 1 2002 1 2003 1 total days 7

Meaning whatever was the day on 30th sep. 1997 itโll repeat on 2003

Therefore, after 1997, next time Mrs.Susheelaโs anniversary will be on same Tuesday on 30th September 2003 Ans A.

Now, How about a CAT level question:

# CAT-2001 Question on calendar

Dec 9, 2001 is Sunday then what was the day on Dec 9, 1971?

1. Thursday
2. Wednesday
3. Saturday
4. Sunday

Same day gain, Day loss

1971 to 2001=how many jumps?

2001-1971=Total 30 years jump

Out of those 30 years, how many leap years?

72, 76,โฆ.,โ00 (multiples of of 4 and 2000 is also leap year because It is multiple of 400)

but no need to manually count leap years.

if you observe

18 x 4 =(19)72

25 x 4 =(20)00

so from 18 to 25 = total 8 leap years. (plz note: 25-18=7 years, but weโve to include both years as wellโฆtherefore.. in such counting, itโll be 25-18+1=8 leap years)

back to the start: 30 years jump and out of them 8 were leap years.

Meaning 22 normal years + 8 leap years = total 30 years

 22 normal years (+1 day gain) 22 x 1 =22 days 8 leap years (+2 days gain) 8 x 2= 16 days total gain 22+16=38 days

38/7=(7×5)+3 remainder

Meaning whatever was the day on Dec 9, 1971, itโll move to +3 days on dec 9 2001

Reverse is also true: Whatever was the day on Dec 2001, itโll be three days less on Dec 9 1971:

Since Dec 2001 was Sunday therefore,

# Question 1988 to 1989

What day of week was it on 5th November,1989ย  if it was Monday on 4th April, 1988 ?

1. Mondayย
2. Tuesday
3. Saturday
4. Sunday

Recall our Day gain Day loss principle

For Non-Leap year, When we proceed forward by one year, then 1 day is gained and vice-versa.

If 4th April, 1988 = Monday, then 4th April, 1989 = Tuesday (Because 1989 is a non-leap year)

Remaining days until 5th Nov.89

 Month Days April (4 to 30) 26 May 31 June 30 July 31 Aug 31 Sep 30 Oct 31 Nov 5 total 215

=Tuesday + 215
Divide 215 with 7 to find the remainder

215=(30*7)+5 Hence five is the remainder

Back to the problem

= Tuesday + [5 days]

What is the 5th day after Tuesday? Count on your fingertip: Wed, Thurs., Fri, Sat., Sunday

# Speed Technique tip#1

in above problem, if you donโt want to waste time in adding the days like 26+31+30โฆ. then use following approach

30 days=(7*4)+2=> 2 remainder

31 days=(7*4)+3=> 3 remainder.

 Month Days Remainder with 7 April (4 to 30) 26 5 (because 26=7*3+5) May 31 3 June 30 2 July 31 3 Aug 31 3 Sep 30 2 Oct 31 3 Nov 5 5 total donโt need 26

Divide this by 7 and find remainder: 26=(7*3)+5 so remainder is 5

=Tuesday + 5

= Tuesday + 5 days

=Sunday

# Speed Technique tip#2

in speed tech #1, if you donโt want to waste time in adding the remainders of seven: 5+3+2โฆ. then do following

pickup remainders that add upto 7 and cancel them.

for example 5+2=7. So Iโll cancel each such pair in the table. Observe

 Month Days Remainder with 7after cancelling numbers that add upto โ7โ (e.g. 5+2) April (4 to 30) 26 5 May 31 3 June 30 2 July 31 3 Aug 31 3 Sep 30 2 Oct 31 3 Nov 5 5 total donโt need 12

After cancelling the two pairs of (5+2), Iโm left with four 3s= 12 (because 4 x 3=12)

=Tuesday + 12

now divide 12 with 7 find remainder: 12=7*1 +5

= Tuesday + 5 days

=Sunday

# Concept: Date Without reference Day

Example: What was the day on 15th August 1947?

To solve this type of questions, youโve to first mug up these two tables:

# Table#1: The odd days

 100 5 200 3 300 1 400, 800, 1200, 1600 etcmultiples of 400 0

^ok but what is the use of above table? It tells us the number of โoddโ days in that given year. I donโt want to bore you with the theory so just mug up those values.

# Tablet #2: Number-Day

 0, 7 Sunday 1 Monday 2 Tuesday 3 Wednesday 4 Thursday 5 Friday 6 Saturday

Just remember that 1 to 6 is Monday to Saturday and 0 or 7=Sunday.

^ok but what is the use of above table? just hang on for a few more paragraphs and youโll know! Now letโs try a sum

# What day of week was on 15th ugust,1947?

Step 1:

Subtract the given year by 1.

1947 -1 = 1946

Step 2:

Break into relevant years as in table #1.

 100 5 200 3 300 1 400, 800, 1200, 1600 etc (multiples of 400) 0

Therefore,

1946 = 1600 + 300 + ( 46 )

Step 3:

Now write corresponding values from the table: 1600=0 and 300=1

1946=>0+1+(46)

Step 4:

Now for the number in bracket (46), divide it by โ4โ and add quotient in same line.

in this case 46=(11x4)+2 therefore, 11 is quotient and 2 is remainder. Weโre concerned with number and quotient here

1946=0+1+(46+11)

Step5:

Now add all these numbers and divide by 7

0+1+(46+11)

=58

And when you divide 58 by 7, you get 58= (7*8)+2. Therefore remainder is 2.

we got the number โ2โ = weโll call this our โ31Dec Numberโ

Observe second table

 0, 7 Sunday 1 Monday 2 Tuesday 3 Wednesday 4 Thursday 5 Friday 6 Saturday

From this table we can see that โ2โ=>Tuesday

It means 31st December 1946 was Tuesday. Now we apply our โ7day cycleโ concept to find out the day on 15th August 1947 using the following formula

Given day= (our 31Dec Number โ2โ)+ *how many days till we reach 15th August?*

Step 6

 from 1st Jan 1947 till we reach 15th August 1947 days in given month Jan 31 feb (not leap year) 28 march 31 april 30 may 31 june 30 july 31 august (upto 15th Aug) 15 total 227 days

back to the โbold partโ

(Our 31Dec Number)+ *how many days till we reach 15th August?*

=2 + 227

=229

Step 7

Divide this number (229) by 7 and whatever remainder you get= that is our day from table #2

229/7=(32*7)+5

so 5 is the remainder and as per table#2

 0, 7 Sunday 1 Monday 2 Tuesday 3 Wednesday 4 Thursday 5 Friday 6 Saturday

5=>Friday.

That means 15th August 1947 was Friday.

# Speed increase tip#1:

in above 15th August example, Back to the step6

31Dec Number+ *how many days till we reach 15th August?*

after that, we did following:

 from 1st Jan 1947 till we reach 15th August 1947 days in given month Jan 31 feb (not leap year) 28 march 31 april 30 may 31 june 30 july 31 august (upto 15th Aug) 15 total 227 days

^as you see we had to sum of 31+28+31โฆ.=lot of time taken in doing the addition (+).

So, it is better to just add remainders for each month with โ7โ

30=(7*4)+2=> 2 remainder

31=(7*4)+3=> 3 remainder.

Now observe again

 from 1st Jan 1947till we reach 15th August 1947 days in given month remainder with 7 Jan 31 3 feb (not leap year) 28 0 march 31 3 april 30 2 may 31 3 june 30 2 july 31 3 august (upto 15th Aug) 15 1 (because 14+1) total 227 days 17

now instead of 227 we can simply write 17

Our 31Dec Number+ *how many days till we reach 15th August?*

=2+17

=19

Therefore 19/7 = its remainder will tell us the final day

19=(7*2) + 5=therefore remainder is 5 and as per table#2, โ5โ means Friday.

# Find the day on 10th May, 1857?

Subtract โ1โ from the given year

1857-1=1856

Now breakup โ1856โ as per our table #1

 100 5 200 3 300 1 400, 800, 1200, 1600 etc (multiples of 400) 0

1856

=1600+200+(56)

write corresponding values from table#1

=0+3+(56)

Divide the bracket number by โ4โ and write quotient along with number

56=14*4 + 0 therefore quotient is 14

1856

=0+3+(56+14)

add these numbers and divide by 7 find remainder

=73/7

=remainder 3

# Speed Technique #3

after doing the division with 4 to find quotient step, you got following

=0+3+(56+14)

Whenever you see the multiple of 7, just scratch that number (because itโll give remainder zero anyways)

for example

=0+3+(56+14)

Here both 56 and 14 are multiples of 7 so even if you divide them by 7, youโre going to get zero as remainder.

=0+3+0+0=3 is 31Dec Number

as per table#2: โ3โ means Wednesday. Meaning 31st December 1856 was Wednesday

now โour 31Dec Numberโ+ โhow many days till 10th May, 1857?โ

 from 1st Jan 1857till we reach 31th May 1857 days in given month remainder with 7 Jan 31 3 feb (not leap year in 1857) 28 0 march 31 3 april 30 2 may 10 3, Because 10=(7 x 1)+3 total *not needed* 11

back to our problem

โour 31Dec Numberโ+ โhow many days till 10th May, 1857?โ

=3 + 11

=14

when 14 is divided by 7 we get zero as remainder.

as per table#2

 0, 7 Sunday 1 Monday 2 Tuesday 3 Wednesday 4 Thursday 5 Friday 6 Saturday

Zero means Sunday. so final answer 10th May 1857 was Sunday.

## Extra facts:

1. The 1st day of a century must be Tuesday, Thursday, or Saturday.
2. The last day of a century cannot be Tuesday, Thursday, or Saturday.

# Mock questions

1. In 2013, Gandhiโs birth-anniversary is on Wednesday. In which nearest future year, will his birth-anniversary be on Monday?
2. If 29th April 2013 is Monday then what is the day on 30th November 2013?
3. If June 11, 2013 is Monday, what was the day on July 11, 2000
4. What was the day on 9/11 attacks in 2001
5. What was the day on 26/11 attacks in 2008

1. 2017
2. 30/nov/13=Saturday
3. 11/jul/00=Monday
4. 11/09/01=Tuesday
5. 26/11/08=Wednesday

For more articles on aptitude, visit Mrunal.org/aptitude

## 165 Comments on “[Reasoning] Calendar Questions: Finding day or date, concepts, shortcuts explained”

1. and black friday in India refers to serial blasts in 1993…visit this link..
en.m.wikipedia.org/wiki/Black_Friday_(1993)

2. Thnk u so much for posting such a tricky article……

3. Which day of week on 19oct 2000

1. 1.The code for 2000(millenium):6
2.The code for october:0
3.The code for 19(day):19(that number itself.You can also use 5 instead of 19 because for a value which is more than 6,you can divide it by 7 and take the reminder as answer.
4.Take the last two digit of the year,2000: 00
Divide it by 4 and take the quotient as answer=00/4=0
5.Take the last two digit of the year,2000
Divide it by 7 and take the reminder as answer=00/7=0

Add 1+2+3+4+5====6+0+19+0+0=25 which is higher than 6.Divide it by 7 ,we get 4 as reminder. 4 represents Thursday(Because day code for sunday=0,monday=1…..etc)

(You can do the method of division by 7 whenever you find with a value which is grater than 6)

I hope you understood …

1. sir, how u r tking code for millenium as 6 and code for October as 0..please elaborate !! ur method is pretty fast if I get dis..!! please elaborate conceptually..

2. you cannot calculate the day for 21 oct 2000 by this method. similarly 21 oct 2001 and many more dates.

4. the day at July 8, 1983. i am unable to calculate,with this method.

1. 1.The code for 1983-which is in 1900+(millenium):0
2.The code for July:6
3.The code for 8(day):8(that number itself) {It is greater than 6,so divide it by 7,and take reminder=1}
4.Take the last two digit of the year,1983: 83
Divide it by 4 and take the quotient as answer=83/4=20+something.Avoid that some thing.Take integers only.ie 20[This value is greater than 6, so divide it by 7 and take the reminder as answer.So it is 6]….Refer earlier problem also….k
5.Take the last two digit of the year,1983
Divide it by 7 and take the reminder as answer=83/7=6

Add 1+2+3+4+5====0+6+1+6+6=19 .Which is greater than 6,so divide it by 7 and take the remider as answer=5 {5 is friday…}
k….

5. Thanking you very much!

6. u take the next yr as referncebut book takes previous yr as refernce..
eg. if 3 Jan, 2008 was Friday then what day was on 3Jan,2009.

According to u : its +1 bcoz 2009 is not leap yr and date falls before Feb so answer is Saturday BUT
According to book : its +2 bcoz 2008 was leap year so answer is Sunday….

Kindly clarify at the earliest..or reply the reasons at smartyanu90@gmail.com

7. july 11 2000, im getting the answer as friday not monday. somebody help

1. July 11 2000 is tuesday yaaar…..

2. may be because you are moving 2 days forward , you will get your answer if you move backward.
solution :
11 june 2013 -monday
from 11 june 2013 to 11 july 2013 – 30 days -> 2 days ahead-> so 11 july 2013 – wednesday

now count difference from 11 july 2000 to 11 july 2013 – 13 years = 3 leap year (don’t count 2000) + 10 normal year= 6+10 = 16 days= 2*7 +2

remainder =2 -> so move 2 step backward from wednesday -> 11 july 2000 – MONDAY

1. nice way of explaining. sorry, but could you explain why 2000 is not counted as a leap year?

8. what is the date of last saturday of working year as well as week.

9. Extra facts:

The 1st day of a century must be Tuesday, Thursday, or Saturday.

I think this is wrong.
For example
1 january 2100 is friday.

10. Your work is even more praiseworthy than super 30″

11. I

12. Sir ..kindly help me out with 4th question as I am not able to solve it

13. I have a query here. With regard to the concept of ‘Date without day reference’, what if in Step 4 the no. in bracket is less than 4 ie.(3) (2) (1) and in Step 5 the no. to be divided by 7 is less than 7 itself? How should we proceed in such a scenario?

14. Here is dr. Rob method it is also easy check out.Here is a standard method suitable for mental computation: (1) Take the last two digits of the year. (2) Divide by 4, discarding any fraction. (3) Add the day of the month. (4) Add the month’s key value: JFM AMJ JAS OND: 144 025 036 146 (5) Subtract 1 for January or February of a leap year. (6) For a Gregorian date, add 0 for 1900’s, 6 for 2000’s, 4 for 1700’s, 2 for 1800’s; for other years, add or subtract multiples of 400. (7) For a Julian date, add 1 for 1700’s, and 1 for every additional century you go back. (8) Add the last two digits of the year. (9) Divide by 7 and take the remainder. Now 1 is Sunday, the first day of the week, 2 is Monday, and so on. Comments by me: (a) You would have to memorize the key values of Step 4. (b) You would have to memorize the century values of Step 6 or 7. (c) A remainder of 0 would give you Saturday at the end. (d) You could cast out 7’s as you go along if you wish, to keep the number small, and then step 9 is redundant. (e) You can do steps (1 and 2), 3, 4, 5, and 6 in any order. As soon as someone starts to tell you the date “July …” you can do step 4, and probably reject doing step 5; then when he says “… 8th…” you can do step 3. When he says “… 19 …” you can do step 6. This makes it seem as though you have done all the calculation after hearing the date, whereas you have done some of it *while* hearing it. The example of July 8, 1954, would go like this: (1) 54 (2) 54/4 = 13 (3) 13 + 8 = 21 (4) 21 + 0 = 21 (5) 21 – 0 = 21 (6) 21 + 0 = 21 (8) 21 + 54 = 75 (9) 75 – 7*10 = 5 Thursday. Casting out 7’s would give: (1) 54 (2) 6 (3) 0 (4) 0 (5) 0 (6) 0 (7) 5 Thursday

15. @Amol ji, i have used your method for calculating 19th oct 2000, but the answr m getting using this Dr Rob method is wrong!! Plz help me.

16. Mrunal sir please brief me how you have done this step while doing Dec 9 1971 sum ?? You have mentioned from 2001 to 1971 there is 30 yrs jump. If we observe 4*18= 1972 & 4*25 = 2000. How you have derived 18 & 25 here plzz elaborate …the rest steps i understood except this one!! Help

17. did u get d answer.?

18. In extra fact 1: The 1st day of a century must be add [Monday], Tuesday, Thursday, or Saturday.

19. Tinkucan completr a piece of work in 50days and sunil can finish same work in60 days tinku take leave on tuesdays and thursdays and sunil take holiday on sundays and saturdays they start there work on 1 march 1971 then how many days it will take for both to complete and on which day??

20. Sir how to calculate the day of 1-1-2003

1. q-1-1-2003?
(stepA=1+stepB=0+stepC=6+steb D=03+stepE=o)=10/7= reminder is 3 hence Wednesday

21. I really thanks full to all the team who is introduce and avail this site…

22. If Ist january is friday of the year 2010 then what is the day of the week of 31th december of the same year?

1. The first day and the last day of the year has same day.So 31st Dec will be on Friday as 1st January is on Friday.

23. I still dont get how do you get monday in the 3rd question… 3 leap years(4,8,12)… 10+3(2) =16… 16/7 gives remainder 2…from monday move back 2 you get saturday…though the answer given is monday and also that trick to find leap years wont work here… right?

24. If the first and the last day of the year is friday then what is the day of the week on 11september

1. its Saturday

25. 1january 1405 ko kaun sa din tha

26. what is the first and last day of the week as per India. which shuld b tajen. i.e. sunday as the last day or first day of the week, exam point of view?

27. If 4 July, 2015 is Saturday then what would be the day on 12 September 2004? I am not able to solve this question with the above given tricks.Please do help me.

28. fathers birthday is celebrated on a sunday in a certain year. A few months later mothers birthday is also celebrated on a sunday. After how many days from fathers birthday could mothers birthday be celebrated?

1. after 273 days

29. THE above method violates when we calculate for calendar 2021.