Concept
We have to find the day of the week on a mentioned date. Certain concepts are defined as under.
Odd Days
The no. of days exceeding the complete no.
of weeks in a duration is the no. of odd days during that duration.
Ordinary Year
An ordinary year has 365 days
Leap Year
A leap year has 366 days. Every year which is divisible by 4 is called a leap year. For example 1200, 1600, 1992, 2004, etc. are all leap years.
Important Remark :
The first year of every century year ending in 00’s but not a multiple of 400 is not considered a leap year. For example 900, 1000, 1100, 1300, 1400, 1500, 1700, 1800, 1900,
2100 are not leap years.
Counting of odd days :
• Every Ordinary year has 365 days = 52 weeks + 1 day \ (ordinary year has 1 odd day)
• Every leap year 366 days = 52 weeks + 2 day \ (leap year has 2 odd day)
• 100 years = 76 ordinary years + 24 leap years (The year 100 is not a leap year)
= 76 odd days + 2 × 24 odd days
⇒ 124 odd days.
= 5 (Remainder) = 05 odd days Similarly,
200 years = 10 odd days = 03 odd days
300 years = 15/7 = 01 odd day
400 years = 20 + (1)/7 = 0 odd day (1 is added as 400 is a leap year)
Similarly,
800, 1200, 1600, 2000, 2400 years contain 0 odd days.
Counting of days :
After counting the odd days, we find the day according to the no. of odd days ® Sunday for 0 odd day. Monday for 01 odd day and so on.
Important notes :
• In an ordinary year, First & last day of the year are the same.
Ex. : If 1 jan is Friday then 31 Dec. will also have Friday.
• For a leap year, If first day is Monday then last day will be Tuesday of the same year.
• Calender year 1 Jan to 31 Dec. Financial year 1 April to 31 March
• The day on which calendar Started i.e., 1 Jan, 001 was Monday.
• In a leap year, February is of 29 days. In an ordinary year, February has 28 days. 
Illustrations :
Ex. : Find the day of the week on 16 January, 1969.
Sol. 1600 years have ‘0’ odd day .........(a)
300 years have ‘1’ odd day .............(b)
68 years have 17 leap years and 51 ordinary years
Thus = (17 × 2 + 51 × 1) = 85 odd days
≅ ’01’ odd day ................(c)
16 january has = ‘2’ odd days ...........(d)
Adding (a) + (b) + (c) + (d),
We get, 0 + 01 + 01 + 02 = 04 odd days
Ans : Thursday
Ex. : Find the day of the week on 18 July, 1776 (leap year)
Sol. : Here 1600 years have ‘0’ odd day ......(a)
100 years have ‘5’ odd day .......(b)
75 years = (18 leap year + 57 ordinary years)
= (18 × 2 + 57 × 1)
= 93 odd days
= (7 × 13 + 2) = ‘2’ odd days ........(c)
Now, the no. of days from 1st january to 18 July, 1776
= 182 + 18 = 200 days
= (28 × 7 + 4) days = ‘4’ odd days ....(d)
Adding (a) + (b) + (c) + (d),
We get, 0 + 5 + 2 + 4 = 04 odd days
Ans. Thursday
Ex. : On what dates of October, 1975 did Tuesday fall ?
Sol. : For determining the dates, we find the day on 1st Oct, 1975
1600 years have ‘0’ odd day ..........(a)
300 years have ‘01’ odd day ............(b)
74 years have (18 leap year + 56 ordinary
years)
2 × 18 + 1 × 56 = 92 odd days
= ‘01’ odd days ..........(c)
Days from 1 st January to 1st Oct., 1975
= 1st Jan to 30 June + 1st July to 1st oct.
181 + 31 + 31 + 30 +1 = 274 days
= ‘01’ odd days ............(d)
(274 / 7 = 01 days)
Adding (a) + (b) + (c) + (d)
= 0 + 01 + 01 + 01 = ‘03’ odd days
Ans. Wednesday (1st Oct), Hence7, 14, 21, 28 Oct. will Tuesday fall.
Ex. : The year next to 1996 having the same Calendar will be -
Sol. : years : 1996 1997 1998
1999 2000
odd days : 2 1 1 1 2
Total odd days = 2 + 1 + 1 + 1 + 2
= 7
= 0 odd days
Hence, year 2001 will have the same calender as year 1996.
Ex. : Prove that last day of a century cannot be
Tuesday, Thursday or Saturday
Sol. : 100 years have = 5 odd day \ Last day
of Ist century is Friday
200 years have = 10 odd day \ Last day
of IInd century is Wednesday
= 3 odd day
300 years have = 15 odd day \ Last day
IIIrd century is Monday
= 01 odd day
400 years have = (5 × 4 + 1) \ Last day
IVth century is Sunday
= 21 odd days
= 0 odd days
Since the order keeps on cycling, we see that the last day of the century cannot be Tuesday, Thursday or Saturday.
Tables : For calculating odd days 
Question. If it was Saturday on 17th November, 1962 what will be the day on 22nd November, 1964 ?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Sunday
Answer: D
Question. Karan was born on Saturday 22nd March 1982. On what day of the week was he 14 years 7 months and 8 days of age ?
(A) Sunday
(B) Tuesday
(C) Wednesday
(D) Monday
Answer: D
Question. If the seventh day of a month is three days earlier than Friday, what day will it be on the nineteenth day of the month ?
(A) Sunday
(B) Monday
(C) Wednesday
(D) Friday
Answer: A
Question. If on 14th day after 5th March be Wednesday, what day of the week fall on 10th Dec. of the same year ?
(A) Friday
(B) Wednesday
(C) Thursday
(D) Tuesday
Answer: B
Question. If 1st October is Sunday, then 1st November of the same year will be :
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
Answer: C
Question. Which of the following year is a leap year?
(A) 1882
(B) 1800
(C) 1296
(D) 1962
Answer: C
Question. If the day before yesterday was Saturday, what day will fall on the day after tomorrow ?
(A) Friday
(B) Thursday
(C) Wednesday
(D) Tuesday
Answer: C
Question. If February 1, 1996 is Wednesday, what day is March 10, 1996 ?
(A) Monday
(B) Sunday
(C) Saturday
(D) Friday
Answer: C
Question. On what dates of August 1980, did Sunday fall ?
(A) 3rd, 10th, 17th, 24th, 31th
(B) 4th, 11th, 18th, 25th
(C) 8th, 13th, 20th, 27th
(D) 2nd, 9th, 16th, 23rd, 30th
Answer: A
Question. If the seventh day of a month is three days earlier than Friday, what day will it be on the nineteenth day of the month ?
(A) Sunday
(B) Monday
(C) Wednesday
(D) Friday
Answer: A
Question. Find the day of the week on 26 January, 1950.
(A) Tuesday
(B) Friday
(C) Wednesday
(D) Thursday
Answer: D
Question. Sangeeta remembers that her father’s birthday was certainly after eighth but before thirteenth of December. Her sister Natasha remembers that their father’s birthday was definitely after ninth but before fourteenth of December. On which date of December was their father’s birthday ?
(A) 10th
(B) 11th
(C) 12th
(D) Data inadequate
Answer: D
Question. What was the day on 20th December,1985 ?
(A) Monday
(B) Tuesday
(C) Thursday
(D) Friday
Answer: D
Question. If 27th January. 1996 was Sunday then what day would be on 26th March, 1997 ?
(A) Monday
(B) Tuesday
(C) Thursday
(D) Sunday
Answer: C
Question. If it was Saturday on 17th December, 1982 what will be the day of 22nd December 1984 ?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Sunday
Answer: D
Question. Sonika is 10 weeks elder than Mala and Mala is 91 days younger than Jyoti. If jyoti was born on Monday then on what day of a week Sonika was born?
(A) Saturday
(B) Sunday
(C) Thrusday
(D) None
Answer: D
Question. How many leap year and ordinary year are there in the first 100 years AD ?
(A) 25, 75
(B) 23, 77
(C) 24, 76
(D) 26, 74
Answer: C
Question. Are the years 900 and 1000 leap years ?
(A) Yes
(B) No
(C) Can’t say
(D) None of these
Answer: B
Question. Which day can not be first day or last day of any centuary ?
(A) Sunday
(B) Monday
(C) Tuesday
(D) Friday
Answer: C
Question. Find the day of the week on 15 August, 1947.
(A) Tuesday
(B) Friday
(C) Wednesday
(D) Thursday
Answer: B
Question. Which two months in a year have the same calendar ?
(A) June, October
(B) April, November
(C) April, July
(D) October, December
Answer: C
Question. If the day before yesterday was Saturday, what day will fall on the day after tomorrow ?
(A) Friday
(B) Thursday
(C) Wednesday
(D) Tuesday
Answer: C
Question. The year that will have the same calender as that of the year 1995 is -
(A) 2002
(B) 2005
(C) 2006
(D) 2001
Answer: C
Question. A baby who was born on 29th Feb. 1896, when did he celebrate his first birthday.
(A) 28th Feb. 1897
(B) 29th Feb. 1900
(C) 29th Feb. 1904
(D) 20th Feb. 1908
Answer: C