Question

If in a particular leap year June month has 5 Mondays which is 1st day of that month possibility, then that year started with which one of the following days?​

Answer 1

Given: If in a particular leap year June month has 5 Mondays which is 1st day of that month possibility.

To find: the year started with which day.

Solution:

Know that, June has a total of 30 days.

Understand that there are two sets of possibilities for having 5 days of mondays. i.e.,

{1 june, 8 june, 15 june, 22 june, 29 june} or {2 june, 9 june, 16 june, 23 june, 30 june}.

Therefore,

 Case 1) When 1 June = Monday, and the year is a leap year.

 Find the day of 1 January.

Odd days $= 31$(May) $+ 30$(April) $+ 31$(March)$+ 29$(Feb.)$+ 31$(Jan.)

                $= 3 + 2 + 3 + 1 + 3$

                $= 12$ odd days

                $= 5$ odd days.

Therefore,  1 January = Monday - 5

                                  = wednesday  

Case 2) When 2 June = Monday, and the year is a leap year.

 Find the day of 1 January.

Odd days$= 1$(June)$+ 31$(May) $+ 30$(April) $+ 31$(March) $+ 29$(Feb.) $+ 31$(Jan.)

                $= 1 + 3 + 2 + 3 + 1 + 3$

               $= 13$odd days

               $= 6$ odd days.

Therefore, 1 January = Monday - 6

                             = Tuesday

Hence, that year started with Tuesday or Wednesday.