# 20. Calendars

Sakshi Education

**Introduction:-**

**Solar Year:**A solar Year consists of 365 days 5 hours 48 minutes 48 sec.

**Leap and Ordinary year:**

A Non-leap year (or) Ordinary year has 365 days, where as a leap year has one extra day because of 29 days in the month of February. Every year which is divisible by 4 is called a leap year. A leap year consists of 366 days (52 weeks + 2 days). There extra 2days are the odd days, so a leap year has 2 odd days. An ordinary year has 1 odd day (52weeks+1day)

**Leap year:**A year which is divisible by 4 is a leap year, except century year which are not multiple of 400.

**Note**: Every century, which is multiple of 400, is a leap year

**Ex:**400, 800, 1200, 1600, 2000…

**Finding the no. of odd days:**

In a given period, the number of days more than the Complete weeks are called odd days.

- One ordinary year = 365 days = (52 weeks + 1 day)

So an ordinary year has 1 odd day

- One leap year = 366 days (52 weeks + 2 days)

So a leap year has 2 odd days

- 100 years = 76 ordinary years + 24 leap year

= (76 × 1 + 24 × 2)

= 124 odd days

= (17 weeks + 5 days) = 5 odd days

No. of odd days in 100 years = 5

No. of odd days in 200 years = 5 + 5 = 10 – 7 = 3 odd days

No. of odd days in 300 years = 5 + 5 + 5 = 15-14 = 1 odd day

No. of odd days in 400 years = 5+ 5 + 5+ 6 = 21-21 = 0 odd days

Similarly 400, 800, 1200, 1600…. Years has 0 odd day

**Codes for the weeks:**

**No. of days**1

2

3

4

5

6

7

**Day**Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

**Codes for the century years:**

100 years – 5

500 -5

900-5

1300-5

1700-5

2100-5

200 years – 3

600-3

1000-3

1400-3

1800-3

2200-3

300 years – 1

700-1

1100-1

1500-1

1900-1

2300-1

400 years – 0

800-0

1200-0

1600-0

2000-1

2400-0

**No. of Odd days in month wise:**

**MONTH****No. of dates****Odd days**January

31

3

February

28/29

0/1

March

31

3

April

30

2

May

31

3

June

30

2

July

31

3

August

31

3

September

30

2

October

31

3

November

30

2

December

31

3

**Solved Examples**

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

**Sol:**16th July, 1776 = (1775 years + period from 1.1.1776 to 16.7.1776)

Counting of odd days:

Number of odd days in 1600 years = 0

Number of odd days in 100 years = 5

75 years = 18 leap years + 57 ordinary years

= (18× 2 + 57 × 1) odd days = 93 odd days

= (13 weeks + 2 days) = 2 odd days

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

Jan.

Feb.

March.

April.

May.

June.

July

(31

+29

+ 31

+30

+ 31

+ 30

+ 16) =

198 days

198 days = (28 weeks +2 days) = 2 odd days.

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

Hence, the required day is Tuesday

**Ex. 2 What was the day of the week on 15th August, 1947?**

**Sol:**15th August, 1947 = (1946 years + period from 1.1.1947 to 15.8.1947)

Odd days in 1600 years = 0

Odd days in 300 years = (5×3) = 15 = 1

46 years = (11 leap years + 35 ordinary years)

= (11× 2 + 35 × 1) odd days = 57 odd days

= (8 weeks + 1 days) = 1 odd day.

Odd days in 1946 years = (0+1+1) =2.

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 = (2+3) = 5

Hence, the required day is Friday.

**Ex. 3 What was the day of the week on 4th June, 2002?**4th June, 2002 = (2001 years + Period from 1.1.2002 to 4.6.2002)

Sol:

Odd days in 1600 years = 0

Odd days in 400 years = 0

Odd days in 1 Ordinary year = 1

Odd days in 2001 years = (0 + 0 +1) = 1

Jan.

Feb.

March

April

May

June

(31

+ 28

+ 31

+ 30

+31

4)

= 155 days

= 22 weeks + 1 day = 1 odd day

Total number of odd days = (1+1) = 2

Required day is Tuesday

**Ex: 4 on what dates of March 2005 did Friday fall?**First we find the day on 1.3.2005

Sol:

1.3.2005 = (2004 years + period from 1.1.2005 to 1.3.2005)

Odd days in 1600 years = 0

Odd days in 400 years = 0

4 years = (1 leap year + 3 ordinary years)

= (1× 2 + 3 ×1) odd days = 5 odd days

Jan.

Feb.

March

(31

+28

+1)

= 60 days = (8 weeks + 4 days) = 4 odd days.

Total number of odd days = (0+0+5+4) = 9 = 2 odd days

.: 1.3.2005 was Tuesday. So, Friday lies on 4.3.2005

Hence, Friday lies on 4th, 11th, 18th and 25th of March, 2005.

**Ex: 5 Prove that the calendar for the year 2003 will serve for the year 2014.**We must have same day on 1.1.2003 and 1.1.2014

Sol.

So, number of odd days between 31.12.2002 and 31.12.2013 must be 0.

This period has 3 leap years and 8 ordinary years.

Number of odd days = (3 × 2 + 8 ×1) = 14 = 0 odd day

:. Calendar for the year 2003 will serve for the year 2014.

**EXERCISE**

**What was the day of the week on 15th Aug, 1947?**

(a) Friday

(b) Sunday

(c) Thursday

(d) Tuesday

(e) Saturday

**How many odd days in 256 days?**

(a) 5

(b) 6

(c) 3

(d) 4

(e) 2

**How many odd days in 15 years?**

(a) 5

(b) 4

(c) 3

(d) 6

(e) 1

**How many odd days in 189 days?**

(a) 0

(b) 2

(c) 3

(d) 4

(e) 5

**What was the day of the week on 21st June 2014?**

(a) Sunday

(b) Friday

(c) Monday

(d) Thursday

(e) Saturday

**If January 1, 2007 was Monday then what day of the week lies on January 1, 2008?**

(a) Tuesday

(b) Sunday

(c) Thursday

(d) Friday

(e) Monday

**If January 1, 2008 was Friday then what day of the week lies on Jan 1, 2010?**

(a) Sunday

(b) Monday

(C) Thursday

(d) Saturday

(e) Friday

**On 6th march, 2005 Monday falls. What was the day of the week on 6th march, 2004?**

(a) Sunday

(b) Saturday

(c) Monday

(d) Tuesday

(e) Friday

**On 05th Feb 2006 Friday falls. What was the day of the week on 5th feb, 2004?**

(a) Thursday

(b) Sunday

(c) Tuesday

(d) Friday

(e) Saturday

**Which of the following is a leap year?**

(a) 1000

(b) 1200

(c) 1400

(d) 1800

(e) 2100

**Which of the following is a non-leap year?**

(a) 1972

(b) 1964

(c) 1976

(d) 1990

(e) 1984

**On what dates of June 2012 did Monday full?**

(a) 4th, 11th, 18th, 25th

(b) 6th, 13th, 20th, 27th

(c) 3rd, 10th, 17th, 24th

(d) 7th, 14th, 21st, 28th

(e) None of the above

**The last day of a century cannot be____**

(a) Monday

(b) Wednesday

(c) Tuesday

(d) Friday

(e) Sunday

**What was the day of the week on 14th march 1969?**

(a) Saturday

(b) Friday

(c) Wednesday

(d) Monday

(e) Sunday

**The Calendar for the year 2014 will be the same for the year?**

(a) 2020

(b) 2021

(c) 2024

(d) 2025

(e) 2026

**The calendar for the year 2013 will be the same for the year?**

(a) 2019

(b) 2018

(c) 2025

(d) 2026

(d) 2026

(e) 2024

**The calendar for the year 1996 will be same for the year?**

(a) 2007

(b) 2024

(c) 2020

(d) 2016

(e) 2012

**The calendar for the year 1999 will be same for the year?**

(a) 2008

(b) 2015

(c) 2010

(d) 2009

(e) 2027

**On what dates of jan 2015 did Friday fall?**

(a) 2nd, 9th, 16th, 23rd, 30th

(b) 2nd, 9th, 16th, 23rd

(c) 4th, 11th, 18th, 25th

(d) 3rd, 10th, 17th, 24th

(e) 7th, 14th, 21st, 28th

**What was the day of the week on 29th Oct 1986?**

(a) Tuesday

(b) Wednesday

(c) Monday

(d) Sunday

(e) Friday

**On 8th march, 2005 it was Tuesday, what was the day of the week on 8th Feb 2004?**

(a) Sunday

(b) Monday

(c) Saturday

(d) Friday

(e) Tuesday

**If 10-May- 2012 is a Friday, What will be the day as 26-August-2016?**

(a) Monday

(b) Sunday

(c) Saturday

(d) Wednesday

(e) Tuesday

**On what days of May 2015 did Friday fall?**

(a) 1St, 8th, 15th, 22nd, 29th

(b) 6th, 13th, 20th, 27th

(c) 5th, 12nd, 19th, 26th

(d) 3rd, 10th, 17th, 24th, 31st

**What was the day of the week on 26th Jan 2015?**

(a) Sunday

(b) Tuesday

(c) Wednesday

(d) Monday

(e) Friday

**What was the day of the week on 6th June 2012?**

(a) Wednesday

(b) Sunday

(c) Monday

(d) Friday

(e) Saturday

**If today is Friday then what will be the day after 189 days?**

(a) Sunday

(b) Thursday

(c) Friday

(d) Saturday

(e) Wednesday

**If today 17-March 2012 is Saturday then what will be the day after 69 days?**

(a) Friday

(b) Monday

(c) Sunday

(d) Tuesday

(e) Saturday

**If today 26-April 2014 was Monday then what will be the day of the date 26-Nov 2013?**

(a) Friday

(b) Thursday

(c) Wednesday

(d) Sunday

(e) Monday

**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

(e) Saturday

**Jan I, 2007 was Monday, what day of the week lies on Jan 1, 2008?**

(a) Monday

(b) Tuesday

(c) Wednesday

(d) Sunday

(e) Thursday

| ||||||

| a |
| d |
| a | |

| d |
| a |
| c | |

| b |
| c |
| a | |

| a |
| b |
| d | |

| e |
| d |
| a | |

| a |
| a |
| c | |

| b |
| b |
| a | |

| a |
| d |
| b | |

| c |
| a |
| d | |

| b |
| b |
| b |

**Prepared by,**

**IACE, Hyderabad**

Published date : 06 Jun 2015 05:18PM