1 ^st day of century can not start with which of the following day?

In a period of 100 years there are 23 or 24 leap (as for century year it might be or might not be a leap leap year, as 1900 was not a leap year)
Number of odd days in a period of 100 years is 100 + 23 or 100 + 24 or 123/124 odd days.
Number of odd days in 100 years is when 123/124 divided by 7, remainder is 4 or 5. So next century should start with Friday or Saturday.

In a period of 100 years there are 23 or 24 leap years (as for century year it might be or might not be a leap leap year, as 1900 was not a leap year)
Number of odd days in a period of 100 years is 100 + 23 or 100 + 24 or 123/124 odd days.
Number of odd days in 100 years is when 123/124 divided by 7, remainder is 4 or 5. So next century should start with Monday or Tuesday.

If there are 53 Saturday and Sunday that means year is a leap year and last day of year and last day of year is Sunday so 1^st day of January must be Saturday then January will have 10 weekends.

Here we have two cases :
Case (i) : If a month start with Thursday the month will have 5 Saturdays and 4 Sundays i.e total 9 weekends. In this case 31^st December will be Sunday hence 1^st January will be either Sunday (For non leap year) or Saturday ( For leap year) then January will have 9 or 10 weekends.
Case (ii) : If a month start with Sunday the month will have 4 Saturdays and 5 Sundays i.e total 9 weekends.
In this case 31^st December will be Wednesday hence 1^st January will be either Wednesday (For non leap year) or Tuesday ( For leap year) then January will have 8 or 9 weekends.
Hence number of weekends in January will be 8 or 9 or 10.

100 years contain 5 odd days.
? Last day of 1^st century is Friday.
200 years contain (5 x 2) = 3 odd days.
? Last day of 2^nd century is Wednesday.
300 years contain ( 5 x 3) = 15 = 1 odd day.
? Last day of 3^rd century is Monday
400 years contain 0 odd day.
? Last day of 4^rd century is Sunday.
This cycle is repeated that means last day of century is Friday, Wednesday, Monday, or Sunday and it repeats the cycle.

If previous year is leap year then calendar of May is similar to July

Let initial quantity of milk & water in the mixture are 5x & 4x
2 litres water is added.
Hence,
New quantity of milk & water will be 5x & (4x+2)
ATQ,
5x/(4x+2) = 10/9
x/(4x+2) = 2/9 9x = 8x + 4
x=4
Hence,
New amount of water in the mixture = 4x+2 = (4*4) + 2 = 18 litres.

Let the weight of vessel be x
Weight of water = 24 ? x
? (24 ? x)/4 + x = 9
? 24 ? x + 4x = 36
? 3x = 12
? x = 4 kg