If the 1st of January of a non-leap year is a Monday, then which one o

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If the 1st of January of a non-leap year is a Monday, then which one of the following days will the 31st of December of that year be ?

Monday
Tuesday
Sunday
None of the above
This question was previously asked in
UPSC CISF-AC-EXE – 2022
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A non-leap year has 365 days. To find the day of the week for the 31st of December given the day of the 1st of January, we need to find the number of odd days between these two dates. The number of days from January 1st to December 31st inclusive is 365.
The number of odd days in a given period is the remainder when the total number of days in the period is divided by 7. A non-leap year has 365 days. Dividing 365 by 7 gives a remainder of 1 (365 = 52 * 7 + 1). Therefore, there is 1 odd day in a non-leap year.
The day of the week repeats every 7 days. The day of the week for the day after the 1st of January will be (Day of 1st Jan + Number of days after 1st Jan) modulo 7, shifted appropriately. The 31st of December is 364 days after the 1st of January (365 total days – 1 day for Jan 1st). 364 days = 52 weeks (364 / 7 = 52). The number of odd days is 364 mod 7 = 0. Thus, the day of the week on December 31st will be the same as the day of the week on January 1st. If January 1st is a Monday, December 31st of a non-leap year will also be a Monday. A leap year has 366 days (52 weeks and 2 days), so the 31st of December in a leap year is one day ahead of the 1st of January.

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