I have Xamarin installed on the Visual Studio 2013 on Windows Operating System. It works fine.
There is Xamarin tools in VS2013 as follows:
My problem
Here is the solution:
I have deleted all the existing versions of visual studio ( 2010, 2012, 2013) except Visual Studio 2015 and then installed the Xamarin, and then I could able to see Xamarin on Visual Studio 2015.