Normal Year: Any year is said to be normal year, if it consists of 365 days in that calendar year.

Leap Year: Any year is said to be leap year, if the year is divisible by 4. There is an exceptional condition that every century year must be divisible by 400, but not with 4. In every leap year, we have 366 days.

Odd Days: The extra or remaining days left over after taking all the weeks is called as Odd Days.

Concept 1:

Finding the Week of the Day for the given Date

If number of odd days are 0 – SUNDAY, 1 – MONDAY, 2 – TUESDAY, 3 – WEDNESDAY, 4 – THURSDAY, 5 – FRIDAY, 6 – SATURDAY.

Eg: 1) What was the day of the week on 15^th August, 1947?

(a) Saturday                   (b) Thursday                  (c) Friday                      (d) Wednesday

2) What was the day of the week on 28^th May, 2006?

(a) Thursday                  (b) Friday                      (c) Saturday                  (d) Sunday

Concept 2:

Problems based on ‘if’ condition

Eg: 1) If, January 16, 1997 was a Thursday. What day of the week will it be on January 4, 2000?

(a) Tuesday                   (b) Thursday                 (c) Wednesday                           (d) Friday

2) If, February 20, 1999 was Saturday. What day of the week was on December 30, 1997?

(a) Tuesday                    (b) Monday                   (c) Thursday                              (d) Data inadequate

Concept 3:

Repetition of Same Calendar Year

1) Every leap year will repeats after 28 years.

2) First year after leap year repeats after 6 years

3) Second year after leap year repeats after 11 years.

4) Third year after leap year repeats after 11 years.

Eg: 1) The year next to 1991 having the same calendar as that of 1991 is:

(a) 1998            (b) 2001           (c) 2002            (d) 2003

2) The year next to 1988 having the same calendar as that of 1988 is:

(a) 1996            (b) 1992            (c) 2012            (d) 2016

What was the day of the week on 18^th August, 1991?

A) Thursday               B) Friday        C) Saturday     D) Sunday       E) Monday       

SOLUTION:

18^th August, 1991 means (1990 years 7 months and 18 days)

1900 years = 1600 years + 300 years = 0 + 1 = 1 odd day.

(Since, every 400 multiples of years have 0 odd days & 300 years have 1 odd day)

1900 years will have 1 odd day.

90 years have 22 leap years and 68 ordinary years

= (22 × 2 + 68 × 1) odd days = 112 = 0 odd days

7 months and 18 days

Jan     Feb     Mar     Apr     May     Jun     Jul     Aug

31       28       31       30        31        30      31       18       

Total days = 230 => 6 odd days

Therefore, total no. of odd days = (1 + 0 + 6) = 7 odd days = 0 odd days.

‘0’ odd days indicates ‘SUNDAY’.

Hence, it was Sunday on 18^th August, 1991.

ANSWER: D

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