Quantitative Aptitude Calendars Study Material
If someone asks you what day it was on IOth May 1575 or what day it would be on 12th September 2340, you may call him crazy for asking such silly questions. If you don’t know the rule how to find it, it may look like a Herculean task for you. But, truly speaking, it is not so difficult. In this chapter we will concentrate our discussion on finding its answer i.e; on what day of the week a particular date falls. The clue to the process of finding it lies in calculating the number of odd days, which is quite different from the odd numbers.
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The number of days more than the complete number of weeks in a given period are called odd days. In other words it is the remainder left when the given number of days is converted into weeks on dividing it by 7.
In ancient times many civilizations used calendars based on movement of the moon. These lunar calendars were not accurate and corrections had to be made frequently. Later, based on the fact that in the solar system all planets including Earth revolved around the Sun, solar calendars were developed. These solar calendars proved to be more accurate. 1
A solar year consists of 365 days, 5 hours, 48 minutes and 48 seconds. In Julian calendar, arranged in 47 BC by Julius Caesar, the year was taken as 365— days. In order to make up for the odd quarter of a day, an extra or intercalary day was added once in every fourth year and this was called 'a Leap year. Thus, an ordinary year consists of 365 days and a leap year has 366 days. In a leap year, February has 29. days instead of 28 days for ordinary year. The calendar based on this system is known as the Old Style Calendar. But, as can be noticed on comparison, since the solar year is 11 minutes 12 seconds less than a quarter of a day, in due course of several years, Julian Calendar too became inaccurate by several days. It again called for a further correction to be made. To rectify this discrepancy Pope Gregory XIII devised another calendar known as Gregorian Calendar. According to it, not all century years are leap years, although all of them are divisible by 4. He made centurial years leap years only once in 4 centuries. Accordingly, only those century years which are divisible by 400 arc leap years, while other century years are ordinary years. For example; 1300, 1400 and 1500 are ordinary years but 1600 is a leap year. With this modification, the Gregorian Calendar came in close exactitude with the solar year and the difference between the two is only 26 seconds which amounts to a day, in 3323 years. These calendars are called as the New Style Calendars.
In India, Vikrami and many other calendars were used earlier. Now the Government of India has adopted the National Calendar based on Sakaera with Chaitra as its first month. The days of this national calendar have a direct permanent correspondence with the days of Gregorian —
Chaitra 1 falls on March 22 in an ordinary year and on March 21 in a leap year.
Points to be Remembered:
1. An ordinary year contains 365 days i.e., 52 weeks and 1 odd day.
2. A leap year contains 366 days i.e., 52 weeks and 2 odd days.
Note : For an year to be a leap year, both the following conditions should be satisfied:
(i) An year divisible by 4 is a leap year. For example, 1984, 1988,1992, 1996,2000etc.
(ii) In case of century years, only those divisible by 400 are leap years, while other century years arc not leap years. For example, 400,800,1200,1600,2000 etc. are leap years.
500, 600,700,900, 1000 etc. are not leap years.
3.100 years contains 24 leap years and 76 ordinary years.
Therefore 100 years :
= [(24 x 52) weeks + (24 x 2) add days) + [(76 x 52) weeks + (76 x 1) odd days)
= (24 + 76) x 52 weeks + (48 + 76) odd days.
= 5200 weeks + 124 odd days.
= 5200 weeks + 17 weeks + 5 odd days.
' = 5217 weeks + 5 odd days. • "
i.e., 100 years contains 5 odd days.
200 years contains (5x2)= 10 =1 week + 3 odd days, i.e., 3 odd days.
300 years contains (5 x 3) = 15 = 2 weeks + 1 odd day, i.e, 1 odd day.
400 years is a leap year and hence it will contain (5 x 4) + 1 = 21 days which equals 3 weeks and and hence no odd day.
Similarly, 800, 1200, 1600, 2000 years each contain no odd day.
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