A vessel, full of water, weighs 24 kg. When the vessel is 1/4 full, it weighs 9 kg. Find the weight of empty vessel.

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.

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

Last day of century can be Friday, Wednesday, Monday, or Sunday and it repeats the cycle. So 1^st day of next century must be either Saturday, Thursday, Tuesday, or Monday and so it must not be Wednesday, friday & Sunday

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.