> If Today is 15th august 2001. And your asked to find the day of the week on 15th august 2017.
> If you don't know the method, it will prove a tough job for you. This type of questions is some times asked in competitive exams.
> The process of finding it lies in obtaining the number of odd days. So we should be familiar with odd days.........
> A week is having seven days from saturday to
Friday : 1 week = 7days
years can be divided into two types
1. Ordinary year (Non-Leap year)
2. Leap year
1. Ordinary year:
> An ordinary year consists of 365 days (52 complete weeks + 1day), the extra one day is the odd day. So, an ordinary year has one odd day.
> Usually ordinary year starts and ends with the same day.
Ex: Since 01-01-2015 is thursday than 31-12- 2015 is also thursday. Similarly
> 01-01-2017 is sunday and 31-0-2017 is also sunday.
> The calender which we are using Gregorian Calender.
> According to this calender 01-01-01 is Monday.
> In ordinary year January and October months having same calender months.
> In ordinary year February, March & November will start with the same day since feb 1, 2017 is wednesday than march 1 & Nov 1 is also wednesday.
> In one year 7 months are having 31 days. 4 months are having 30 days. 1 Month is having 28 or 29 days
Leap year:
A leap year is having 366 days i.e., 52 weeks & 2 odd days.
Usually a leap year starts with friday and ends with saturday
Century year: If the year is exactly divided by two then that year is called century year.
Ex: 100, 200, 300, . . . . . . 1000, 2000 .... etc.
Except century year, if remaining all the years are exactly divisible by 4 than that year is called leap year, if not it is non-leap year
Ex: 1016, 1020, 2012, 2036...... leap years 890, 2003, 2015, 2017....... Non leap years
If century year us exactly divisible by 400, than that year is said to be a leap year if not Non-leap year
Ex: 2000 it is leap year 400, 800, 1200, 1600, 2000......... 1700, 1100, 200, 1500 ..... non leap years
> Usually century year does not end with Tuesday, Thurs day and saturday.
> Century year starts with Monday or Tuesday or Thursday or Saturday.
> In a leap year January and July months are having same calender months.
> The remainder is said to be number of odd days by dividing the given days by 7. 7+7+7+7+3 = 31days 7+7+7+7+2 = 30days
Counting the number of odd days:
1. One ordinary year = 365 days = 52 weeks + 1 day therefore, one ordinary year has one odd day.
2. One leap year = 366 days = 52 weeks + 2 days. therefore, one leap year has 2 odd days.
3. 100 years consist of 24 leap years + 76 ordinary years. (100 years when divided by 4, we get 25 leap years i.e., the 100th year is not leap year, hence only 24 leap years) = 76 ordinary years + 24 leap years = ((76x52) weeks +76 days) + ((24x52) weeks + 24x2 days) = 5200 weeks + 124 days = 5200 weeks + 17 weeks + 5days = 5217 weeks + 5 days therefore,
> The extra 5 days are the number of odd days. So, 100 years contain 5 odd days Similarly, for 200 years we have 5x2 = 10 extra days = 1 week + 3 days. therefore, 200 years contain 3 odd days. similarly, 300 year contain 1 odd day and 400 years contain 0 odd days. Similarly 800, 1200 ete... contain no odd day.
Example: 1. Imagine that in a calendar year, there were 436 days and 9days in a week, then how many odd days will be there in that year?
a. 1
b. 2
c. 3
d. 4
Ans: d
Explanation: Dividing 436 by 9 we get 4 as a reminder.
therefore, required odd days are 4. 2. How many odd days are there in 382 days. a. 4 b. 3 c. 2 d. 1 Ans: a
Explanation:
> Dividing 382 by 7 we get 4 as a reminder.
> It shows required odd days.
Day > Sat
Code > 0
Day > Sun
Code > 1
Day > Mon
Code > 2
Day > Tue
Code > 3
Day > Wed
Code > 4
Day > Thur
Code > 5
Day > Fri
Code > 6
Century 1500-1599 > 0 Code
Century 1600-1699 > 6 Code
Century 1700-1799 > 4 Code
Century 1800-1899 > 2 Code
Century 1900-1999 > 0 Code
Century 2000-2099 > 6 Code
Century 2100-2199 > 4 Code
Century 2200-2299 > 2 Code
J F M = 1 4 4 (122 = 144)
A M J = 0 2 5 (52 = 025)
J A S = 0 3 6 (62 = 036)
O N D = 1 4 6 (122 + 2 = 144+2 = 146)
Formula: (Date + Month Code + No of years + No of leap years + Century code)/7
Note: We have to take the remainder after dividing this. To find out the No of leap year we have to consider the Quotient.
Type -1:
1. What day of the week was Aug 15, 1947.
Ans: (15+3+47+11+0)/7 76/7 = 6 Its Friday
2. What day of the week was 24 feb, 2017.
Ans: (24+4+17+4+6)/7 55/7 = 6 (Reminder after dividing 55 by 7) Its Friday.
3. What was the day of the week on Jan 1,2017.
Ans: (1+1+17+4+6)/7 29/7 = 1 Its Sunday
4. What was the day of the week 14th feb 2012.
Ans: (14+4+12+3+6)/7 39/7 = 4 Required date = 4-1 = 3 Its Tuesday
Note: If the given year is leap year and the day is in the month of January and February we have to reduce the remainder by 1.
1. What will be the day of the date 29-08-2020.
Ans: (29+3+20+5+6)/7 63/7 = 0 Its Saturday
Type-2:
1. If 9th Jan 2009 was Sunday than find the day of the week on 12th April 2017.
Ans: First we have to find actual date of 9th January 2009 = (9+1+9+2+6)/7 = 27/7 = 6 (Friday)
= 6+(2) = Sunday
Now we have to find actual date of
= 12th April 2017
= (12+0+17+4+6)/7
= 39/7 = 4 (Wednesday)
= 4+2 = 6 Friday
2. If 22nd April, 1982 Thursday then what day of the week was 3rd Nov 1982?
Ans: 22nd April 1982
(22+0+82+20+0)/7
124/7 = 5 (Thursday)
3rd Nov 1982
(3+4+82+20+0)/7
109/7 = 4 (Wednesday)
Type-3:
1. On which dates of Jan 2017 will be a Friday come?
Ans: First we have to find the day on 1-1-2017
(1+1+17+4+6)/7
59/7 = 1 (Sunday)
01 Jan is Sunday then 6th Jan is Friday
6+7 = 13
13+7 = 20
20+7 = 27
2. Find the date of second saturday in the month of september 2013.
a. 14th Sep
b. 13th Sep
c. 12th Sep
d. 11th Sep
Ans: a
Explanation:
> First we have to find the date of the day 01-09- 2013 = (1+6+13+3+6)/7 = 29/7 = 1 (Sunday)
> According to the problem we have to find saturdays.
> We know that Sunday + 6 = Saturday
> So September 1 is sunday than september 7th become 1st saturday. Therefore, September 14th is second saturday...... similarly third saturday falls on september 21st and last saturday falls on september 28th
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