What three numbers, none of which is zero, give the same result whether they’re added or multiplied?

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

While house hunting in London, I came across a very good leasehold property Discussing the lease the landlady told me:

'The property was originally on a 99 years lease and two-thirds of the time passed is equal to four-fifths of the time to come. Now work it out for yourself and see how many years are to go!

A mathematics teacher took exams for his students. Out of the total students, 25% passed both the tests included in the exam. However, only 42% were able to clear the first test.

Can you find out the percentage of those students who passed the first test and also passed the second test?

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?

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

A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

There is a box. The area of its top is 240 square units, the area of the front is 300 square units and the area of the end is 180 square units.

Can you calculate the dimensions of this box with the given data?