Synopsis IAS

Answer

Solution

UPSC Prelims

Mathematics

Theme:

Clocks and Calendars / घड़ी और कैलेंडर

Q7 2022, Clocks and Calendars

Which date of June 2099 among the following is Sunday?

We know that January 01, 2001 is Monday and December 31, 2000 is a Sunday (It is a fact).

There are 98 complete years + 5 months (Jan 2099 to May 2099) + One day of June (i.e. June 1)

98 complete years have 24 leap years having 2 odd days each and 74 ordinary years having one odd day each.

So total number of odd days in 98 years = 24×2 + 74×1 = 48 + 74 = 122 (i.e. 122/7 = 3 odd days).

In year 2099 (Ordinary Year, having Feb of 28 days) Jan to May we will get number of days as follows 3 (Jan) + 0 (Feb) + 3 (March) + 2 (April) + 3 (May) + 1 (June) = 3 + 3 + 2 + 3 + 1 = 12 = 5 odd days (12/7)

Q 7. 2022, Clocks and Calendars