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# CHAPTER – 6

CALENDARS
Suppose you are asked to find the day of the week on Counting number of odd days, when two dates
30th June, 1974, it would be a tough job to find it if you do are given:
not know the method. The method of finding the day of
the week lies in the number of "odd days". Any month which has 31 days has 3 odd days.
( Q 31 ÷ 7 leaves 3 as remainder) and any month which
Note: Every 7th day will be the same day count has 30 days has 2 odd days (30 ÷ 7 leaves
wise, i.e. if today is Monday, then the 2 as remainder).
7th day counting from Tuesday onwards
will once again be Monday. Odd day is Then, the total number of odd days are calculated by
the days remaining after completion of an adding the odd days for each month. The value so
exact number of weeks. Odd day is the obtained is again divided by 7 to get the final number of
reminder obtained on dividing the total odd days. The day of the week of the second date is
number of days with seven. obtained by adding the odd days to the day of the week
of the earlier date.
Example: 52 days ÷ 7 = 3 odd days.
Examples:
Leap and Non-leap Year:
1. If you were born on 14th April, 1992, which was a
A Non- leap year has 365 days whereas a leap year has Sunday, then on which day of the week does your
one extra day because of 29 days in the month of birthday fall in 1993?
February. Every year which is divisible by 4 is called a (A) Monday (B) Tuesday
leap year. Leap year consists of 366 days, (C) Wednesday (D) Friday
(52 complete weeks + 2 days), the extra two days are (E) Thursday
the odd days. So, a leap year has two odd days.
Sol: 14th April 1992 to 14th April 1993 is a complete
An non-leap year consists of 365 days year, which has 365 days. Hence, the number of
(52 complete weeks + 1 day). The extra one day is the odd days from 14th April 1992 to 14th April 1993 is
odd day. 1. Hence, 14th April 1993 is one day after Sunday
i.e., Monday. Choice (A)
Note: Every century, year which is a multiple of
400, is a leap year. A century year which 2. If 1st Jan, 1992 is a Tuesday then on which day of
is not divisible by 400 is a non-leap year. the week will 1st Jan, 1993 fall?
(A) Wednesday (B) Thursday
Example: 400, 800, 1200, 1600 …. are leap years. (C) Friday (D) Saturday
500, 700, 900, 1900 … are non-leap years. (E) Tuesday

Counting the number of Odd Days: Sol: Since 1992 is a leap year there are 2 odd days.
Hence, 1st January 1992 is two days after
100 years consist of 24 leap years + 76 ordinary years. Tuesday i.e., Thursday. Choice (B)
(100 years when divided by 4, we get 25. But at the 100th
year is not a leap year, hence only 24 leap years). 3. If 1st April, 2003 was Monday, then which day of the
week will 25th December of the same year be?
= 2 x 24 odd days + 1 x 76 odd days
(A) Tuesday (B) Wednesday
= 124 days
(C) Thursday (D) Friday
= 17 weeks + 5 days (E) Monday
The extra 5 days are the odd days.
So, 100 years contain 5 odd days.
Sol: The number of days from 1st April to
Similarly, for 200 years we have 10 extra days 25th December
(1 week + 3 days). (29 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 25) days
∴ 200 years contains 3 odd days. = 268 days
Similarly, 300 years contain 1 odd day and 400 years 268
contain 0 odd days. = = 38 + 2 odd days .
7
Hence, 25th December is two days after Monday,
Counting of number of odd days, when only i.e., Wednesday. Choice (B)
one date is given:
4. On which day of the week does 4th June,
Here we take January 1st 1 AD as the earlier date and 2001 fall?
we assume that this day is a Monday. We take its (A) Monday (B) Tuesday
previous day, i.e. Sunday as the reference day. After this (C) Wednesday (D) Thursday
the above mentioned method is applied to count the (E) Friday
number of odd days and find the day of the week for the
given date.
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Sol: 4th June 2001 ⇒ (2000) years + 1st January to Hence, 2011 will have the same calendar as that
4th June 2001. of 2005. Choice (D)
We know that 2000 years have zero odd days.
The number of odd days from 1st January to 6. What day of the week was 18th April 1901?
4th June 2001. (A) Monday (B) Tuesday
Month : Jan + Feb + Mar + Apr + May + June (C) Wednesday (D) Friday
Odd day: 3 + 0 + 3 + 2 + 3 + 4 (E) Thursday
15
= 1 odd day. Sol: 18th April 1901 ⇒ (1600 + 300) years +
7
1st January to 18th April 1901.
Hence, 4th June 2001 was a Monday.
1600 years have – 0 odd days
Choice (A)
300 years have – 1 odd day
The number of days from 1st January, 1901 to 18th
5. Which year will have the same calendar as that of
April 1901 is (31 + 28 + 31 + 18) days
2005?
(A) 2006 (B) 2007 108 days ≅ 3 odd days
(C) 2008 (D) 2011 ∴ Total number of odd days = 3 + 1 = 4
(E) 2012 Hence, 18th April 1901 is Thursday.
Choice (E)
Sol: Year: 2005+2006+2007+2008+2009+2010
Odd days : 1+ 1+ 1+ 2+ 1 + 1
Total number of odd days from 2005 to 2010 are
7 ≅ 0 odd days.

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Exercise – 6
Directions for questions 1 to 25: Select the correct alternative from the given choices.

1. If 8th February 1995 was a Wednesday, then 13. The last day of a century cannot be
8th February 1994 was on which day? (A) Friday (B) Wednesday
(A) Wednesday (B) Thursday (C) Monday (D) Tuesday
(C) Friday (D) Monday (E) Sunday
(E) Tuesday
14. Which day of the week was 25th December, 1995?
2. If 17th September 1993 was a Friday, then which day
of the week was 30th June 1989? (A) Sunday (B) Monday
(A) Wednesday (B) Thursday (C) Tuesday (D) Wednesday
(C) Friday (D) Saturday (E) None of these
(E) Tuesday
15. Which day of the week was 23rd July 1776?
3. If 11th August 1985 was a Sunday, that which day of (A) Sunday (B) Wednesday
the week was 13th August 1986? (C) Thursday (D) Tuesday
(A) Tuesday (B) Monday (E) Monday
(C) Thursday (D) Friday
(E) Wednesday
16. If holidays are declared only on Sundays and in a
particular year 12th March is a Sunday, is
4. How many odd days are there in 352 days?
23rd September in that year a holiday?
(A) 1 (B) 2 (C) 3
(D) zero (E) 4 (A) Yes
(B) No
5. Which among the following years is a leap year? (C) Yes, if it is a leap year.
(A) 3000 (B) 3100 (C) 3200 (D) No, if it is a leap year.
(D) 3300 (E) 3500 (E) Cannot be determined

6. If 1st January 2012 is a Sunday, then which day of 17. Which day of the week was 1601, Jan 15?
the week will the new year be celebrated in 2016? (A) Monday (B) Tuesday
(A) Friday (B) Sunday (C) Wednesday (D) Thursday
(C) Wednesday (D) Saturday (E) Friday
(E) Thursday
18. The first Republic day was celebrated on
7. If 1st April 1963 was a Monday, then which day of 26th Jan 1950. It was a
the week will 1st August 1959 be? (A) Thursday (B) Friday
(A) Wednesday (C) Monday (D) Tuesday
(B) Monday (E) Wednesday
(C) Tuesday
(D) Thursday 19. If 23rd April 2006 is a Sunday, then 23rd April
(E) Saturday 2106 will be a
(A) Wednesday (B) Thursday
8. On which dates of October, 1994 did Monday fall? (C) Friday (D) Saturday
(A) 4, 11, 18, 25 (B) 2, 9, 16, 23 (E) Sunday
(C) 1, 8, 15, 22 (D) 3, 10, 17, 24, 31
(E) 5,12,19,26 20. If the first day of the years 2012 and 2023 are
Mondays, which day of the week will the last days of
years be respectively?
9. Which year will have same calendar as 2002?
(A) Tuesday, Tuesday
(A) 2008 (B) 2011 (C) 2009 (B) Tuesday, Monday
(D) 2013 (E) 2015 (C) Monday, Tuesday
(D) Sunday, Monday
10. Which year will have same calendar as 1984? (E) Tuesday, Wednesday
(A) 2020 (B) 2008 (C) 2012
(D) 2004 (E) 2006 21. If 14th November 2006 is a Sunday, then
14th November 2706 is a
11. What will be next leap year after 2096? (A) Sunday (B) Friday
(A) 2100 (B) 2101 (C) 2104 (C) Tuesday (D) Monday
(D) 2108 (E) 2106 (E) Wednesday

12. If in a calendar year, there are 541 days and 22. In a year, if 23rd November is a Friday then
10 days a week, then how many odd days will be 14th March in that year is on which day of the week?
there in that year? (A) Monday (B) Wednesday
(A) 1 (B) 2 (C) 3 (C) Sunday (D) Tuesday
(D) 4 (D) Zero (E) Saturday

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23. In a leap year, which month will have the same 25. Which day of the week is 21st April 2006?
calendar as that of January in that year? (A) Tuesday (B) Wednesday
(A) April (B) July (C) Thursday (D) Monday
(C) October (D) March (E) Friday
(E) June

## 24. What is the next leap year after 2396?

(A) 2398 (B) 2408 (C) 2404
(D) 2400 (E) 2412

Key
1. E 6. A 11. C 16. B 21. D
2. C 7. E 12. A 17. A 22. B
3. E 8. D 13. D 18. A 23. B
4. B 9. D 14. B 19. C 24. D
5. C 10. C 15. D 20. B 25. E

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