If 3rd March falls on Monday of a year then on which day 26th September and 22nd July fall.Explain
Answers
Answer:
Tuesday 22nd July
Friday 26th September
Step-by-step explanation:
Let's write [month] for the "number of days in said month". So [Apr] = 30 and [Mar] = 31.
To get from 3rd March to 3rd April, we need to advance [Mar] days.
Then [Apr] days to 3rd May. And so on.
So
number of days from 3rd March to 22nd July
= ( number of days from 3rd Mar to 3rd July ) + ( number of days from 3rd July to 22nd July)
= ( [Mar] + [Apr] + [May] + [Jun] ) + (22 - 3)
= 31 + 30 + 31 + 30 + 19.
But for every multiple of 7 days, we end up on the same week day, so advancing 31 days has the same effect as advancing 3 days, in terms of "day of week". So we can safely remove multiples of 7 and we get
day of week after 31 + 30 + 31 + 30 + 19 days
= day of week after 3 + 2 + 3 + 2 + 5 days
= day of week after 15 days
= day of week after 1 day
So 22nd July, being 31+30+31+30+19 days later, is on the same day of the week as it will be 1 day later. That is, it will be a Tuesday.
Doing the same for 26th September:
days to 26th Sep
= days to 3rd Sep + (days from 3rd to 26th)
= [Mar] + [Apr] + [May] + [Jun] + [Jul] + [Aug] + (26 - 3)
= 31 + 30 + 31 + 30 + 31 + 31 + 23
which has the same effect on week day as (removing multiples of 7)
3 + 2 + 3 + 2 + 3 + 3 + 2 = 18,
and this has the same effect has advancing 4 days.
Thus 26th September will be on a Friday.