Why we chosen our typical working frequency is 50 Hz or 60 Hz? Why not any other numbers?

Early electrical systems included 25 Hz (it learn itself to the speed ratings of early industries, such as steel production) and 40 Hz. We obtain more 'power per unit volume of material' at higher frequencies, but the eddy-current losses increase as the square of the frequency. 50 and 60 Hz systems won out.
Similarly, there were abundant 2-phase systems in the Northeastern US during those early days. There are still pockets of 25 Hz, 40 Hz, and even 2-phase in use today.

60 Hz was the result of engineering tradeoffs, I think made by or influenced by Nicolai Tesla. He was one of the early proponents of distributing AC, as apposed to Edison who wanted to distribute DC. The tradeoff had to do with size of the machines and transformers needed, which get smaller with higher frequency, and some losses, which go up with frequency. I remember reading that some careful study went into the decision to pick 60 Hz.

50 Hz, on the other hand, was due to marketing. There was a german manufacturer of power grid equipment that wanted to distinguish themselves and managed to get 50 Hz pushed thru as the standard in Germany and then much of Europe. This meant they didn't have to compete with the American 60 Hz equipment. The rest of the world ended up with 60 or 50 Hz depending on who they bought their equipment from and whether they were more economically tied to Europe or or the US. Since Russia adopted the European 50 Hz standard, the soviet block all became 50 Hz countries.