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?

Can you find the largest Three-digit number whose sum is 14 and whose square is less than 5,00,000?

Can you make the number 24 by utilizing the numbers 1, 3, 4 and 6? You must use one number only one time and you can use mathematical operation symbols anytime anywhere.

'S' refers to the number of seconds in a day and 'H' refers to the number of hours in ten years. Which quantity out of these two is greater?

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.

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.

If nine thousand, nine hundred nine dollars is written as $9,909,
how should twelve thousand, twelve hundred twelve dollars be written?

Use the digits from 1 up to 9 and make 100.

Follow the rules.
=> Each digit should be used only once.
=> You can only use addition.
=> For making a number, two single digits can be combined (for example, 4 and 2 can be combined to form 42 or 24)
=> A fraction can also be made by combining the two single digits (for example, 4 and 2 can be combined to form 4/2 or 2/4)

Question: how can we do this?

How can I get the answer 24 by only using the numbers 8,8,3,3?

You can use the main signs add, subtract multiply and divide.

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *