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##C#, 252 247 245 232 216 Bytes ##

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

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

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

• Saved 5 Bytes thanks to @FryAmTheEggman
• Saved 2 Bytes thanks to @theLambGoat
• Saved 7 Bytes by removing static from class p
• Saved 24 Bytes thanks to @milk