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

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

Using Only Five 5's and any mathematical operator make sum as 37

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?

A newspaper is supposed to have 60 pages.Pages 14 and 21 are missing from the newspaper.

Can you tell me , Which other pages won't be there as well ?

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

Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209

Our product and our sum always give the same answer. Who are we?

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?