CALENDAR GENERAL QUESTIONS
Calendar – Formulas
1. Odd Days:
We are supposed to find the day of the week on a given date.
For this, we use the concept of 'odd days'.
In a given period, the number of days more than the complete weeks are called odd days.
2. Leap Year:
(i). Every year divisible by 4 is a leap year, if it is not a century.
(ii). Every 4th century is a leap year and no other century is a leap year.
Note: A leap year has 366 days.
Examples:
i. Each of the years 1948, 2004, 1676 etc. is a leap year.
ii. Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
iii. None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.
3. Ordinary Year:
The year which is not a leap year is called an ordinary years. An ordinary year has 365 days.
4. Counting of Odd Days:
1. 1 ordinary year = 365 days = (52 weeks + 1 day.)
= 1 ordinary year has 1 odd day.
2. 1 leap year = 366 days = (52 weeks + 2 days)
= 1 leap year has 2 odd days.
3. 100 years = 76 ordinary years + 24 leap years
= (76 x 1 + 24 x 2) odd days = 124 odd days.
= (17 weeks + days) = 5 odd days.
= Number of odd days in 100 years = 5.
Number of odd days in 200 years = (5 x 2) = 3 odd days.
Number of odd days in 300 years = (5 x 3) = 1 odd day.
Number of odd days in 400 years = (5 x 4 + 1) = 0 odd day.
Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.
5. Day of the Week Related to Odd Days:
No. of days: | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
Day: | Sun. | Mon. | Tues. | Wed. | Thurs. | Fri. | Sat. |
ਇਸ ਸੈਕਸ਼ਨ ਵਿੱਚ ਅਸੀਂ ਸਾਲ, ਮਹੀਨਿਆਂ, ਹਫ਼ਤਿਆਂ, ਦਿਨਾਂ ਆਦਿ ਦੇ ਸੰਬੰਧ ਵਿੱਚ ਚਰਚਾ ਕਰਾਂਗੇ, ਸਾਡੇ ਕੋਲ ਹੇਠ ਲਿਖੀ ਮਹੱਤਵਪੂਰਨ ਜਾਣਕਾਰੀ ਹੈ :
·
ਇਕ ਹਫ਼ਤੇ ਵਿੱਚ 7 ਦਿਨ ਹੁੰਦੇ ਹਨ : ਸੋਮਵਾਰ, ਮੰਗਲਵਾਰ, ਬੁੱਧਵਾਰ, ਵੀਰਵਾਰ, ਸ਼ੁੱਕਰਵਾਰ,
ਸ਼ਨੀਵਾਰ ਅਤੇ ਐਤਵਾਰ!
·
ਇਕ ਸਾਲ ਵਿੱਚ 12 ਮਹੀਨੇ ਹੁੰਦੇ ਹਨ: ਜਨਵਰੀ, ਫਰਵਰੀ, ਮਾਰਚ, ਅਪ੍ਰੈਲ, ਮਈ, ਜੂਨ, ਜੁਲਾਈ, ਅਗਸਤ, ਸਤੰਬਰ, ਅਕਤੂਬਰ, ਨਵੰਬਰ ਅਤੇ ਦਸੰਬਰ।
·
31 ਦਿਨਾਂ ਵਾਲੇ
ਮਹੀਨੇ : ਜਨਵਰੀ, ਮਾਰਚ, ਮਈ, ਜੁਲਾਈ, ਅਗਸਤ, ਅਕਤੂਬਰ ਅਤੇ ਦਸੰਬਰ
ਮਹੀਨਿਆਂ ਵਿੱਚ 31 ਦਿਨ ਹੁੰਦੇ ਹਨ।
·
30 ਦਿਨਾਂ ਵਾਲੇ
ਮਹੀਨੇ : ਅਪ੍ਰੈਲ, ਜੂਨ, ਸਤੰਬਰ ਅਤੇ ਨਵੰਬਰ ਮਹੀਨਿਅ ਦੇ 30 ਦਿਨ ਹੁੰਦੇ ਹਨ।
·
28 ਜਾਂ 29 ਦਿਨਾਂ ਵਾਲਾ ਮਹੀਨਾ : ਗੈਰ ਲੀਪ ਸਾਲ ਵਿੱਚ ਫਰਵਰੀ ਵਿੱਚ 28 ਦਿਨ ਹੁੰਦੇ ਹਨ। ਲੀਪ ਵਾਲੇ ਸਾਲ ਵਿੱਚ ਫਰਵਰੀ 'ਚ 29 ਦਿਨ ਹੁੰਦੇ ਹਨ।
·
ਕੈਲੰਡਰ ਸਾਲ : ਇਹ
ਜਨਵਰੀ ਤੋਂ ਸ਼ੁਰੂ ਹੁੰਦਾ ਹੈ ਅਤੇ ਦਸੰਬਰ ਵਿੱਚ ਖ਼ਤਮ ਹੁੰਦਾ ਹੈ।
·
ਵਿੱਤੀ ਸਾਲ : ਇਹ
ਪਹਿਲੀ ਅਪ੍ਰੈਲ ਤੋਂ ਸ਼ੁਰੂ ਹੁੰਦਾ ਹੈ ਅਤੇ 31 ਮਾਰਚ ਨੂੰ ਖ਼ਤਮ
ਹੁੰਦਾ ਹੈ।
·
ਹਫ਼ਤੇ ਦਾ ਪਹਿਲਾ
ਦਿਨ : ਆਮ ਤੌਰ 'ਤੇ ਐਤਵਾਰ ਹਫ਼ਤੇ ਦਾ ਪਹਿਲਾ
ਦਿਨ ਹੁੰਦਾ ਹੈ।
·
ਲੀਪ ਅਤੇ ਗੈਰ ਲੀਪ
ਦਾ ਸਾਲ : ਇਕ ਲੀਪ ਸਾਲ ਵਿੱਚ 366 ਦਿਨ ਹੁੰਦੇ ਹਨ
ਅਰਥਾਤ 52 ਹਫ਼ਤੇ ਅਤੇ 2 'ਦਿਨ। ਜਿਹੜਾ ਸਾਲ 4 ਨਾਲ ਵਿਭਾਜਿਤ ਹੋ ਜਾਂਦਾ ਹੈ
ਉਸ ਨੂੰ ਲੀਪ ਸਾਲ ਕਹਿੰਦੇ ਹਨ। ਨਾਨ ਲੀਪ ਸਾਲ ਵਿੱਚ 365 ਦਿਨ ਹੁੰਦੇ ਹਨ ਅਰਥਾਤ 52 ਹਫ਼ਤੇ ਅਤੇ ਇਕ
ਦਿਨ।
·
100 ਸਾਲ ਵਿੱਚ 76 ਸਾਧਾਰਨ ਸਾਲ, 24 ਲੀਪ ਸਾਲ ਅਤੇ 5 ਵਿਖਮ ਦਿਨ ਹਨ।
·
200 ਸਾਲਾਂ ਵਿੱਚ = (5 × 2 = 10/7) = 3 ਵਿਖਮ ਦਿਨ
·
300 ਸਾਲਾਂ ਵਿੱਚ = (5 × 3 =
15/7) = 1 ਵਿਖਮ ਦਿਨ
·
400 ਸਾਲਾਂ ਵਿੱਚ = (5 × 4 =
20/7) = 0 ਵਿਖਮ ਦਿਨ
|
ਸਮਾਂ |
ਸਾਧਾਰਨ ਸਾਲ |
ਲੀਪ ਸਾਲ |
100 ਸਾਲ |
200 ਸਾਲ |
300 ਸਾਲ |
400 ਸਾਲ |
|
ਵਿਖਮ ਦਿਨਾਂ ਦੀ ਸੰਖਿਆ |
1 |
2 |
5 |
3 |
1 |
0 |
·
ਨਾਨ ਲੀਪ ਸਾਲ ਦਾ ਪਹਿਲਾ ਅਤੇ ਅੰਤਿਮ ਦਿਨ ਉਹੀ ਹੁੰਦਾ ਹੈ।(ਜੇਕਰ 1 ਜਨਵਰੀ ਨੂੰ
ਵੀਰਵਾਰ ਹੈ ਤਾਂ 31 ਦਸੰਬਰ ਨੂੰ ਵੀ ਵੀਰਵਾਰ ਹੋਵੇਗਾ ।)
·
ਲੀਪ ਸਾਲ ਦਾ ਪਹਿਲਾ
ਅਤੇ ਅੰਤਿਮ ਦਿਨ ਇਕ ਵੱਧ ਜਾਂਦਾ ਹੈ।
·
7 ਦਿਨਾਂ ਬਾਅਦ ਦਿਨ ਦੋਹਰਾਇਆ ਜਾਂਦਾ ਹੈ।
|
ਮਹੀਨਾ |
ਵਿਖਮ ਦਿਨ |
|
ਜਨਵਰੀ |
3 |
|
ਫਰਵਰੀ |
0 |
|
ਮਾਰਚ |
3 |
|
ਅਪ੍ਰੈਲ |
2 |
|
ਮਈ |
3 |
|
ਜੂਨ |
2 |
|
ਜੁਲਾਈ |
3 |
|
ਅਗਸਤ |
3 |
|
ਸਤੰਬਰ |
2 |
|
ਅਕਤੂਬਰ |
3 |
|
ਨਵੰਬਰ |
2 |
|
ਦਸੰਬਰ |
3 |
·
ਮਹੀਨੇ ਦੇ ਵਿਖਮ ਦਿਨ
·
ਐਤਵਾਰ ਨੂੰ 0 ਵਿਖਮ ਦਿਨ, ਸੋਮਵਾਰ ਨੂੰ 01ਵਿਖਮ ਦਿਨ ਲਿਖਿਆ ਜਾਵੇ।
·
ਸਾਡੇ ਲਈ 12 ਮਹੀਨਿਆਂ ਦੇ ਵਿਖਮ ਦਿਨ ਹਨ।
1.It was
Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
A.Sunday
B.Saturday
C.Friday
D.Wednesday
Answer: Option-C
Explanation:
On 31st December, 2005 it was
Saturday.
Number of odd days from the year 2006 to the year
2009 = (1 + 1 + 2 + 1) = 5 days.
On
31st December 2009, it was
Thursday.
Thus, on 1st Jan, 2010 it is Friday.
2.What was the day of the week on
28th May, 2006?
A.Thursday
B.Friday
C.Saturday
D.Sunday
Answer: Option-D
Explanation:
28 May, 2006 = (2005 years +
Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years = (4 ordinary years + 1 leap year) = (4 x 1
+ 1 x 2) = 6
odd days
Jan.
Feb. March April May (31 + 28 + 31 + 30 + 28 ) = 148 days
148 days = (21 weeks + 1 day) = 1
odd day.
Total number of odd days = (0 + 0 + 6 + 1) =
7 = 0
odd day.
Given day is Sunday.
3.What was the day of the week on
17th June, 1998?
A.Monday
B.Tuesday
C.Wednesday
D.Thursday
Answer: Option-C
Explanation:
17th June, 1998 = (1997 years +
Period from 1.1.1998 to 17.6.1998)
Odd days in 1600 years = 0
Odd days in 300 years = (5 x 3) = 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121
= 2 odd days.
Jan. Feb. March
April May June (31 + 28 + 31 + 30 + 31 + 17) = 168 days
168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.
4.What will be the day of the
week 15th August, 2010?
A.Sunday
B.Monday
C.Tuesday
D.Friday
Answer: Option-A
Explanation:
15th August, 2010 = (2009 years
+ Period 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 x
2 + 7 x 1) = 11 odd days = 4
odd days.
Jan.
Feb. March April May June July Aug. (31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) =
227 days
227 days = (32 weeks + 3 days) = 3
odd days.
Total number of odd days = (0 + 0 + 4 + 3) =
7 = 0
odd days.
Given day is Sunday.
5.Today is Monday. After 61 days,
it will be:
A.Wednesday
B.Saturday
C.Tuesday
D.Thursday
Answer: Option-B
Explanation:
Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
After 61 days, it will be Saturday.
6.If 6th March, 2005 is Monday, what
was the day of the week on 6th March, 2004?
A.Sunday
B.Saturday
C.Tuesday
D.Wednesday
Answer: Option-A
Explanation:
The year 2004 is a leap year. So, it has 2 odd
days.
But, Feb 2004 not included because we are
calculating from March 2004 to March 2005. So it has 1 odd day only.
The
day on 6th March, 2005 will be 1 day
beyond the day on 6th March, 2004.
Given
that, 6th March, 2005 is Monday.
6th March, 2004 is Sunday (1
day before to 6th March, 2005).
7.On what dates of April, 2001
did Wednesday fall?
A.1st, 8th, 15th, 22nd, 29th
B.2nd, 9th, 16th, 23rd, 30th
C.3rd, 10th, 17th, 24th
D.4th, 11th, 18th, 25th
Answer: Option-D
Explanation:
We shall
find the day on 1st April, 2001.
1st April, 2001 = (2000 years +
Period from 1.1.2001 to 1.4.2001)
Odd days in 1600 years = 0
Odd days in 400 years = 0
Jan. Feb.
March April
(31 + 28 + 31 + 1) = 91 days = 0
odd days.
Total number of odd days = (0 + 0 + 0) = 0
On 1st April, 2001 it was Sunday.
In April, 2001 Wednesday falls on
4th, 11th, 18th and 25th.
8.How many days are there
in x weeks x days?
A.7x2
B.8x
C.14x
D.7
Answer: Option-B
Explanation:
x weeks x days = (7x + x) days = 8x days.
9.The last day of a century
cannot be
A.Monday
B.Wednesday
C.Tuesday
Friday
Answer: Option-C
Explanation:
100 years contain 5 odd days.
Last
day of 1st century is Friday.
200 years contain (5 x 2) = 3
odd days.
Last
day of 2nd century is Wednesday.
300 years contain (5 x 3) = 15 = 1
odd day.
Last
day of 3rd century is Monday.
400 years contain 0 odd day.
Last
day of 4th century is Sunday.
This cycle is repeated.
Last day of a century cannot be Tuesday or
Thursday or Saturday.
10.On 8th Feb, 2005 it was Tuesday.
What was the day of the week on 8th Feb, 2004?
A.Tuesday
B.Monday
C.Sunday
D.Wednesday
Answer: Option-C
Explanation:
The year 2004 is a leap year. It has 2 odd days.
The day
on 8th Feb, 2004 is 2 days before
the day on 8th Feb, 2005.
Hence, this day is Sunday.
11.The
calendar for the year 2007 will be the same for the year:
A.2014
B.2016
C.2017
D.2018
Answer: Option-D
Explanation:
Count the number of odd days from the year 2007
onwards to get the sum equal to 0 odd day.
Year
: 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Odd day : 1 2 1 1 1 2
1 1 1 2 1
Sum = 14 odd days = 0
odd days.
Calendar for the year 2018 will be the same
as for the year 2007.
12.Which of the following is not
a leap year?
A.700
B.800
C.1200
D.2000
Answer: Option-A
Explanation:
The century divisible by 400 is a leap year.
The year 700 is not a leap year.
13.On 8th Dec, 2007 Saturday falls.
What day of the week was it on 8th Dec, 2006?
A.Sunday
B.Thursday
C.Tuesday
D.Friday
Answer: Option-D
Explanation:
The year 2006 is an ordinary year. So, it has 1 odd
day.
So, the
day on 8th Dec, 2007 will be 1 day
beyond the day on 8th Dec, 2006.
But, 8th Dec, 2007 is Saturday.
8th Dec, 2006 is Friday.
14.January 1, 2008 is Tuesday.
What day of the week lies on Jan 1, 2009?
A.Monday
B.Wednesday
C.Thursday
D.Sunday
Answer: Option-C
Explanation:
The year 2008 is a leap year. So, it has 2 odd
days.
1st day of the year 2008 is
Tuesday (Given)
So, 1st day of the year 2009 is 2
days beyond Tuesday.
Hence, it will be Thursday.
15.January 1, 2007 was Monday.
What day of the week lies on Jan. 1, 2008?
A.Monday
B.Tuesday
C.Wednesday
D.Sunday
Answer: Option-B
Explanation:
The year 2007 is an ordinary year. So, it has 1 odd
day.
1st day of the year 2007 was
Monday.
1st day of the year 2008 will be 1 day beyond Monday.
Hence, it will be Tuesday.