Apptitude

# Calendar (How to Find day on Given Date)

Here we will deal with finding the day of the week on a particular date. The process lies on obtaining the no. of odd days.

Odd Days :- In a given period, number of days more than a complete weeks are called odd days.

Leap Year :- Every year which is divisible by 4 is called a leap year. Thus 1992,1996,2004 etc. are leap years. Every 4th century is a leap year like 400,800,1200 etc. but no other century is a leap year like 1500,1900,2100 etc.

An year which is not a leap year is called an ordinary year.

1. An ordinary year has 365 days.
2. A leap year has 366 days.

Counting of odd days :

1 ordinary year = 365 days

= 52 weeks + 1 day

= 1 odd day.

1 leap year = 366 days

= 52 weeks + 2 day

= 2 odd days.

100 years = 76 ordinary years + 24 leap years

= (76 x 52) + 76 days + (24 x 52) + 48 days

= 124 days = 124/7 = 5 odd days

100 years = 5 odd days

200 years = (5+5)/7 = 3 odd days

300 years = (5+5+5)/7 = 1 odd day

400 years = 21 = 0 odd days

(7n+m) odd days, where m<7 is equivalent to m odd days. Thus 8 odd days = 1 odd day.

Lets understand the concept of finding odd days and the day on a particular week by some examples.

Example :- What was the day on 15 August 1947 ?

Solution :- 15 august 1947 = (1946 years + Period from 1 january 1947 to 15 august 1947)

Counting of odd days:

1600 years + 300 years + 47 years

1600 years = 0 odd days.

300 years = 1 odd day.

47 years = 11 leap year + 36 ordinary year

= 11 x 2 + 36 = 58 = 58/7 = 2 odd days.

Jan.     Feb.      March        April       May       June     July        Aug.

31     +   28   +    31     +       30   +     31   +      30     +   31      +    15

= 227 days = 32 weeks + 3 days = 3 odd days

Total No. of odd days = 0+1+2+3 = 6 odd days

Hence , the required day was Saturday.

Example :- What was the day on 16 April 2000 ?

Solution = 16 April 2000 = (1999 year + Period from 1 january 2000 to 16 april 2000)

Counting of odd days:

1600 years + 300 years + 99 years

1600 years = 0 odd day.

300 year = 1 odd day

99 year = 24 leap year + 75 ordinary year

=(24 x 1 + 75 x 2)  = 123 odd days = 123/7 = 4 odd days

Jan.     Feb.      March        April

31     +   29  +    31     +       16

= 107 days = 15 weeks + 2 days = 2 odd days.

Total no. of odd days = 0+1+4+2 = 7 odd days = 0 odd days.

Hence, the required day was Monday.

If you want to test what you have learnt then Click Here..!!

In case anyone of you have any doubt let us know in the comment box below.

### Shubham Lashkan

Myself Shubham an computer science engineer with lots of dream having an unseen attitude with lots of thoughts

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### About Shubham Lashkan

Myself Shubham an computer science engineer with lots of dream having an unseen attitude with lots of thoughts
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