Calendar questions

Quantitative aptitude plays a major role in any competitive exam. Calendar questions are an important part of quantitative-based exams. These questions are usually easy but tricky and time-consuming at the same time. To ease the process, here are some calendar questions with answers that will help you to brush up on your Quantitative Aptitude skills.

1. How many leap years are there in 100 years?

There are two conditions for a leap year:

Century Years (ending with two 0s, example 2000, 2100, 2200.) Non Century Years (not ending with two 0s, example 2001, 2002, 2003) If the century year is divisible by 400, it is a leap year. Hence 2000 is a leap year and 2100 is not a leap year.

If the non century year is divisible by 4, it is a leap year. Hence, 1996 is a leap year whereas 1997, 1998, 1999 are not leap years.

Now, for 100 years there are supposed to be 25 leap years (4, 8, 12, … , 100).

But 100 is a century year and it is not divisible by 400. Hence, 100 is not a leap year and the last leap year in 100 years is the year 96.

Hence, we have (25 - 1 = 24) leap years, if we exclude the year 100.

1. The last day of a century cannot be \(\textit\).

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.

1. If every seconds Saturday and all Sundays are holidays in a 30 days month beginning on Saturday, then how many working days are there in that month ? (Month starts from Saturday)

As month begins on Saturday, so 2nd, 9th, 16th, 23rd, 30th days will be Sundays. While 8th day is second Saturday. Thus, there are 6 holidays in all.

Hence, no. of working days = 30 – 6 =24

1. If the day before yesterday was monday, what day it will fall on the day after tomorrow?

Day before yesterday monday means today is wednesday. So day after tomorrow will be friday.

1. What was the day of the week on 28th May, 2006?

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)=\((4 \times 1+ 1 \times 2 ) \)
= 6 odd days
Days from January 1 to May 28=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

1. How many weeks are there in a normal Year?

22 weeks and 1 day

52 weeks and 1 day

In a normal year there are 365 days, so there will be 52 weeks and 1 day.

1. The last day of a century can be

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 can be Friday, Wednesday, Monday and Sunday.

1. If today is Tuesday, then what will be the day after 50 days?

If today is tuesday, then after 7 days it will occur again. For further occurrence this day will occur also after 14, 21, 28…days.

So, according to the question:

Hence after 49 days tuesday will occur.

and on 50th day, it will be wednesday

1. On what dates of July.2004 did Monday fall?

5th, 12th, 19th, 26th

Let us find the day on 1st July, 2004.

2000 years have 0 odd day. 3 ordinary years have 3 odd days.
Jan. Feb. March April May June July \(31 + 29 + 31 + 30 + 31 + 30 + 1 = 183 days \)
(26 weeks + 1 day) = 1 .
Total number of odd days = \((0 + 3 + 1)\) odd days = 4 odd days.
1st July 2004 was 'Thursday'.
Thus, 1st Monday in July 2004 as on 5th July.

Hence, during July 2004, Monday fell on 5th, 12th, 19th and 26th.

1. Which of the following year is not a leap year?

The two conditions that decide that a year is a leap year or not is:

• For a year to be a leap year, it should be divisible by 4.
• No century is a leap year unless it is divisible by 400.

Hence, the year 2100 is not a leap year as it is not divisible by 400.

1. If 6th March, 2004 was Sunnday, what will the day of the week on 6th March, 2005?

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.

1. Ajay’s birthday is on Friday 20th March. On what day of the week will be sanjay’s Birthday in the same year if sanjay was born on 20th September?

Number of days between 20th March and 20th September:

11 + 30 + 31 + 30 + 31 + 31 + 20 = 184

So, 184 ÷ 7 = 2 odd days

Friday + 2 = sunday

1. The maximum gap between two successive leap year is?

This can be illustrated with an example. Ex: 1896 is a leap year. The next leap year comes in 1904 (1900 is not a leap year).
For a century year to be a leap year it has to be divisible by 400.

1. If 5th March, 2009 is Monday, what was the day of the week on 5th March, 2008?

The year 2008 is a leap year.

So, it has 2 odd days.

But, Feb 2008 not included because we are calculating from March 2008 to March 2009. So it has 1 odd day only.

Given that, 5th March, 2009 is Monday.

5th March, 2008 is Sunday (1 day before to 5th March, 2009).

1. It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

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.

1. The last day of a century cannot be either I. Tuesday II. Thursday III. Saturday IV. Sunday

• Ans. (c)
• The last day of a century cannot be either Tuesday, Thursday or Saturday.

1. The second day of a month having 30 days is Sunday, What will be the last day of the next month which has 31 days ?

As the 2nd day is Sunday, so the first day is Saturday

So, total we have 30+31 = 61 days = 8 weeks + 5 odd days

So, Saturday+5 = Thursday.

1. It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2008?

On Dec 31, 2005, it was Saturday.
No. odd days for the years 2006 and 2007
= Remainder of \(\frac\) = 2 odd days
On Dec 31, 2007 it has to be Monday
Thus on Jan 1, 2008 it is Tuesday.

1. If today is Wednesday then after 105 days what day of the week will it be ?

Dividing 105 by 7 we get 105/7 = 15
No remainder =>no odd days
After 105 days it will be again Wednesday.

1. The calendar for the year 2007 will be the same for the year:

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
respectively

Sum = 14 odd days ≡ 0 odd days. ∴ Calendar for the year 2018 will be the same as for the year 2007.

1. If today is Friday ,what will be the day 282 days from now ?

282 = \( (40\times 7)+ 2 \)

So, 280th day is Friday .

Hence 282th day is Sunday.

Last day of a century cannot be Tuesday or Thursday or Saturday.

1. What was the day on 16th August 1947 if 1st January 2017 was a Sunday.

None of the above

• Days from 16th August 1947 to 1st January 2017

\( 16 + 30 + 31 + 30 + 31 + 18 \) leap years + \( 51 \) years

\( 138 + 18\times366 + 51\times365 \) days

\( 138 + 6588 + 18615 \)days = \( 25341 \)days

\(\frac = 3620 \) weeks + 1 day

To go in past Sunday - 1 = Saturday

16th August 1947 was a Saturday.

1. The calendar for the year 1993 will be same for the year:

To repeat a year there should be no odd days

1993 has 365 days
means \((52\times7)+1\)means 1 odd day
Odd day = In a given period,the number of days more than the complete weeks are called odd days.

Which means if 1 January 1993 is Sunday,then 1 January 1994 will be Monday.

1993 - 1 odd day

1994 - 1 odd day

1995- 1 odd days

Now total 7 odd days mean 0 odd days .

So 1999 will show same Calder as 1993 .

1. On what dates of April 2001 did Wednesday fall?

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.

1. How many leap years and ordinary years are there in a century?

24 leap years and 74 ordinary years

22 leap years and 74 ordinary years

24 leap years and 76 ordinary years

26 leap years and 74 ordinary years

100 , 200 ,etc will not be a leap year

so there are 24 leap years

100- 24= 76 years.

So In a century we have 24 leap years and 76 ordinary years.

1. It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2009?

On 31st December, 2005 it was Saturday. Number of odd days from the year 2006 to the year 2008 = (1 + 1 + 2 ) = 4 days.
On 31st December 2008, it was Wednesday. Thus, on 1st Jan, 2009 it is Thursday.

1. If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?

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, \( 2005 \))

1. If the third day of a month is three days before Sunday, which day will be the 27th day of that month?

If the third day of a month is three days before a Sunday, the Sunday of that month will be on the 6th.

27th day = Sunday

1. Calendar for the year 2014 will be same for the year

Count the number of odd days from 2014 to get sum equal to 0 odd day

sum = 14 odd days = 0 odd day

so 2025 is same as 2014

1. Today is Monday. After 61 days, it will be:

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.

1. What was the day of the week on, 16th July, 1776?

16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)

Counting of odd days :

1600 years have 0 odd day.

100 years have 5 odd days.

75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days

1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.

Jan Feb Mar Apr May Jun Jul

31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 2 days)

Total number of odd days = (0 + 2) = 2.

Required day was 'Tuesday'.

1. Prove that any date in April of a year is the same day of the week corresponding date in July that year.

None of the above

We will show that the number of odd days between last day of March and last day of June is zero. .

= 91 days = 13 weeks = 0 odd day. ,Number of odd days during this period = 0.

Thus, 1st April of an year will be the same day as 1st July of that year. Hence, the result follows

1. It was Sunday on Jan 1, 2010. What was the day of the week Jan 1, 2014?

On 31st December, 2009 it was Saturday.
Number of odd days from the year 2010 to the year 2013 = (1 + 1 + 2 + 1) = 5 days.
On 31st December 2013, it was Thursday.
Thus, on 1st Jan, 2014 it is Friday.

1. Which two months in a year have the same calendar ?

If the period between the two months is divisible by 7, then that two months will have the same calendar.

(a) Oct + Nov \( = 31 + 30 = 61 \) (not divisible by 7)

(b). Apr + May + Jun + Jul + Aug + Sep + Oct \( = 30 + 31 + 30 + 31 + 31 + 30 + 31 = 214 \)(not divisible by 7)

(c) Jun + July + Aug + Sep \( = 30 + 31 + 31 + 30 = 122 \)(not divisible by 7)

(d) Apr + May + June \( = 30 + 31 + 30 = 91 \) (divisible by 7)

Hence, April and July months will have the same calendar.

1. How many leap years will be there in 800 years?

In 100 years, leap year =24 years.

Therefore, in 800 years, leap years will be =8 × 24 = 192

Now, since the leap year occurs once after every four years, means the 400th year and 800th also leap years.

So, the total number of leap years in 800 years=192 + 2 = 194

Hence, option A is the correct answer.

1. If 13th March 2018 was Tuesday then what was the day on 13th March 2021?

We know that in 365 days we have 1 odd day and in 366 days we have 2 odd days.

13 March 2018 = Tuesday

13 March 2019 = Wednesday

13 March 2020 = Friday

13 March 2021 = Saturday.

1. The second day of a month is Sunday, What will be the last day of the next month which has 31 days ?

Can't be determined

We cannot find out the answer because the number of days of the current month is not given.

1. Sahil 's birthday is on Monday, 10 March. On what day of the week will be Anand's Birthday in the same year if Anand was born on 8 August?

Odd days from 10th March to 8th August:
Remaining days in March = 21
Odd days in April = 2
Odd days in May = 3
Odd days in June = 2
Odd days in July = 3
Given day in August = 8
Total odd days = (21 + 2 + 3 + 2 + 3 + 8) ÷ 7
= 39 ÷ 7
= 4
So Monday + 4 =Friday

1. If the fourth day of a month is Wednesday, then which day will come on the third day after the 19th day of the same month?

The fourth day of the month is Wednesday

so, the first day of the month = Sunday

The third day after the 19th day of the month = the 22nd day of the month

1st day of the month = 8th day of the month = 15th day of the month = 22nd day of the month = Sunday.

1. Republic Day of India was celebrated on Thursday in 2017. On which day it was celebrated in 2021?

We know that in 365 days we have 1 odd day.

26 January 2017 = Thursday

26 January 2018 = Friday

26 January 2019 = Saturday

26 January 2020 = Sunday.

2020 is a leap year so February has 29 days.

26 January 2021 = Sunday + 2 = Tuesday (+2 because of leap year, In 366 days we have 2 odd days)

1. What is the year next to 1990 which will have the same calendar as that of the year 1990?

For a year to have the same calendar with 1990 ,total odd days from 1990 should be 0.

Take the year 1992 from the given choices. Total odd days in the period 1990-1991= 2 normal years ≡ 2 x 1 = 2 odd days

Take the year 1995 from the given choices.

Number of odd days in the period 1990-1994 = 4 normal years + 1 leap year ≡ 4 x 1 + 1 x 2 = 6 odd days

Take the year 1996 from the given choices.

Number of odd days in the period 1990-1995= 5 normal years + 1 leap year ≡ 5 x 1 + 1 x 2 = 7 odd days ≡ 0 odd days (As we can reduce multiples of 7 from odd days which will not change anything)

Though number of odd days in the period 1990-1995 is 0, there is a catch here. 1990 is not a leap year whereas 1996 is a leap year. Hence calendar for 1990 and 1996 will never be the same.

Take the year 2001 from the given choices.

Number of odd days in the period 1990-2000= 8 normal years + 3 leap years ≡ 8 x 1 + 3 x 2 = 14 odd days ≡ 0 odd days Also, both 1990 and 2001 are normal years. Hence 1990 will have the same calendar as that of 2001

1. If there is X weeks and X days, how many days are there in total?