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.

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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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