What is both possible and impossible at the same time?

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?

Take away the whole and some still remain. What is it?

What is the below Rebus indicate?

What is common among 11, 69, and 88?

What Deficiency does the below rebus represent?

VIT_MIN

The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?

How many words can a quill made with the feather of a pigeon write with a 100ml bottle of black ink?

You are in a room that has three switches and a closed door. The switches control three light bulbs on the other side of the door. Once you open the door, you may never touch the switches again. How can you definitively tell which switch is connected to each of the light bulbs?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.