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.

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

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

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

Divide 110 into two parts so that one will be 150 per cent of the other. What are the 2 numbers?

If we add four times the age of John four years from now to five times his age five years from now we get ten times his current age.

How old will John be two years from now?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

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?

If 21x = 79x, what is the value of x?

Find three whole, positive numbers that have the same answer when multiplied together as when added together.

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?