aptitude questions on calendar

INTRODUCTION:
There are two types of years, such as:
(i) Ordinary year.
(ii) Leap year.
Ordinary year: It consists of 365 days. In terms of weeks, it consists of 52 weeks and the remainder is 1 which is 1 odd day.
Leap year: The non-century years which are divisible by 4 and the century years divisible by 400 are leap years. It contains 52 weeks and 2 odd days.

The number of odd days in 100 years are 5.
The number of odd days in 200 years are 3.
The number of odd days in 300 years are 1.
The number of odd days in 400 years are 0.

METHOD TO FIND OUT DAY:
To find out the day, we have to find out the number of odd days according to the following 4 steps:
Step I: Number of odd days in the passed century.
Step II: Number of odd days in the passed year.
Step III: Number of odd days in the continuing year in terms of month wise..
Step IV: Number of odd days in the continuing month till the exact day.



Finally
if the number of odd day is 1, it is Monday.
if the number of odd day is 2, it is Tuesday.
if the number of odd day is 3, it is Wednesday.
if the number of odd day is 4, it is Thursday.
if the number of odd day is 5, it is Friday.
if the number of odd day is 6, it is Saturday.
if the number of odd day is 0, it is Sunday.



EXAMPLE:
Find out the day on 9th June 1971.
Solution:
In 1900, the number of odd day is 1.
In70 years, the number of odd days are as follows:
If all 70 years are ordinary years, the number of odd days are 70, but out of 70 years 17 are leap years in which 17 odd days more i.e. 87 odd days and finally 3 odd days.
According to month wise Jan 3, Feb 0, Mar 3, Apr 2, May 3, so finally it is 4.
According to date wise, the number of odd day is 2.
Finally, the number of odd day is 3 that’s why the day is Wednesday.

QUESTION:
Smt Indira Gandhi died on 31st oct 1984. What was that day?
SOL: In 1900, the number of odd days is 1.
In 83 yrs, the number of odd days is 5.
According to month wise from Jan to Sept, the number of odd day is 3+1+3+2+3+2+3+3+2=22 i.e.1.
Date wise up to 31, it is 3.
So the total number of odd day 10 and finally it is 3.
So the day was Wednesday.



If today is Tuesday, then after 65 days it will be which day?
Solution:
In 65 days, there are9 weeks and 2 odd days
So the day will be 2 days ahead of Tuesday i.e. Thursday.


If 2nd April 1983 is on Wednesday, then 2nd April 1987 will be on which day?
Solution:
In this case the asking day is exactly 4 years after the 1st day.
In 4 years, the number of odd days i.e. 5.
So the day will be 5 days ahead of Wednesday i.e. Monday.


sample test:


1.It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

A.Sunday B. Saturday
C.Friday D. Wednesday
....................................
2.

What was the day of the week on 28th May, 2006?
A. Thursday B.Friday
C. Saturday D. Sunday
.........................................

3.

Today is Monday. After 61 days, it will be:?
A. Wednesday B. Saturday
C. Tuesday D. Thursday
................................................

---------------------------Answers---------------------------------------------------
1.
Answer: Option C

Explanation:

On 31st December, 2005 it was Saturday.

Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.

On 31st December 2009, it was Thursday.

Thus, on 1st Jan, 2010 it is Friday.


........................................
Answer: Option D

Explanation:

28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)

Odd days in 1600 years = 0

Odd days in 400 years = 0

5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days

Jan. Feb. March April May
(31 + 28 + 31 + 30 + 28 ) = 148 days

148 days = (21 weeks + 1 day) 1 odd day.

Total number of odd days = (0 + 0 + 6 + 1) = 7 0 odd day.

Given day is Sunday.
..............................................

3.
Answer: Option B

Explanation:

Each day of the week is repeated after 7 days.

So, after 63 days, it will be Monday.

After 61 days, it will be Saturday.