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?

निम्नलिखित में से जून 2099 के किस दिनांक को रविवार होगा?

Explanation Please wait..

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

Total number of odd days between December 31, 2000 to June 1 2099:-

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)

So, total odd days = 3 + 5 = 8 = 1 (remainder when we divide 8 by 7)

Thus June 1, 2099 will be Monday. (considering 31 dec 2000 as base)

So, first Sunday of June will be on 7th.

व्याख्या Please wait..

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