##C# - 252 Bytes ##

The size is pretty bad compared to the other solutions but nevertheless...

    using System;using System.Linq;static class p{static void Main(){string c="";char[]i=Console.ReadLine().ToCharArray();Random r=new Random();for(int b=0;b<i.Count();++b){int d;Console.Write((char)(i[b]+(d=r.Next(10))));c+=d;}Console.WriteLine("\n"+c);}}

This is my second ever answer to a codegolf and I'm quite a beginner considering C# so I'd appreciate to hear how to get it shorter :)

Ungolfed:

    using System;
    using System.Linq;

    static class p
    {
        static void Main()
        {
            string c = "";
            char[] i = Console.ReadLine().ToCharArray();
            Random r = new Random();
            for (int b = 0; b < i.Count(); ++b)
            {
                int d;
                Console.Write((char)(i[b] + (d = r.Next(10))));
                c += d;
            }
            Console.WriteLine("\n" + c);
        }
    }