I'm curious, and I would like to know how much may it cost to build a software more or less similar to the one used for Badoo or Person.com social networks? How much approximate time may it take to build?
It depends on many factors.
1. Programing language, for different languages you need to pay different hostings rates.
Example: for development in PHP are lower hourly rates then in Java.
Note: chosing language is always tricky thing because all changes and updates and "power" of your site depends on that.
2. Design. If you want this to work you need very good design, that involves designe for all platforms so it takes good amount of time so you will pay good money there too.
3. Functionality. How many functions your website will have are thry going to be the same or you will change them.
4. Metodology of work. There are many metodologies in development and it depends on that too.
5. Country. You may ask how the hell county take in count, it counts and that is main thing. Developers in different countries have different standards of life and if you pick somebody from USA or India price will be different. And difference is realy big.
6. Experience. Different developers/designers have different experience so if you hire somebody with more experience you will pay more.
That is my point of view in developing system that you need to take into count.
If you want my estimation for time and money you can ask me in PM.