The last day of a century cannot be

If the period between the two months is divisible by 7, then that two months will have the same calender .

Now,
(a). October + November = 31 + 30 = 61 (not divisible by 7)

(b). Apr. + May + June + July + Aug. + Sep. + Oct. = 30 + 31 + 30 + 31 + 31 +30 + 31 = 213 (not divisible by 7)

(c). June + July + Aug. + Sep. = 30 + 31 + 31 + 30 = 122 (not divisible by 7)

(d). Apr. + May + June = 30 + 31 + 30 = 91 (divisible by 7)

Hence, April and July months will have the same calendar.

The day of the week repeats every 7 days.

Given today is Friday. Again Friday is repeated on the 7th day, 14th,... on 7 multiple days.

Hence, Friday is on the 63rd day, as 63 is multiple of 7.

Now, the required day of the week on the 65th day is Sunday.

Calculating Age has 2 conditions. Let your Birthday is on January 1st.

1. If the month in which you are born is completed in the present year i.e, your birthday, then

Your Age = Present year - Year you are born 

As of now, present year = 2018

i.e, Age = 2018 - 1995 = 23 years.

2. If the month in which you are born is not completed in the present year i.e, your birthday, then

Your Age = Last year - Year you are born

As of now, present year = 2018

i.e, Age = 2017 - 1995 = 22 years.

How to find the years which have the same Calendars :

Leap year calendar repeats every 28 years.

Here 28 is distributed as 6 + 11 + 11.

Rules:

a) If given year is at 1st position after Leap year then next repeated calendar year is Givenyear+6.

b) If given year is at 2nd position after Leap year then next repeated calendar year is Givenyear+11.

c) If given year is at 3rd position after Leap year then next repeated calendar year is Givenyear+11.

Now, the given year is 2018

We know that 2016 is a Leap year.

2016    2017    2018    2019  2020

Lp Y      1st     2nd      3rd     Lp Y

Here 2018 is at 2 nd position after the Leap year.

According to rule b) the calendar of 2018 is repeated for the year is 2018 + 11 = 2029.