The necessity of Extension methods in .NET

The Solution 1 by SAKryukov and Solution 2 by Mohammad A Rahman to the question referred in the above question are very good.

I think the following may be some of the reasons for introduction of Extension methods.

If the static method is to be called then purpose of the method and to which classes it is applicable is to be remembered. Whereas with the extension methods it is easy to recognize as these are available as if they are instance methods of the object concerned.

The extension methods are available in the Intellisense on the objects.
Note: For string object the IEnumerable interface's extension methods are not shown in the intellisense as given in the MSDN documentation. However, the IEnumerable interface's methods can be used on string object also.

The main use of Extension methods is in LINQ. There are around 40 methods on IEnumerable interface for LINQ. Most of the methods return a collection implementing the IEnumerable interface. This enables the fluent syntax, so that different operations can be executed in a chain. Let us see an example as shown below:

void Main()
{
    List<int> marks = new List<int>{
        35,61, 90,65,40,70,72,95,45,55,60,76,92,65,50,75,61,74};
    var marksRange = marks.Select (m =>
                new {
                    No = m < 50 ? 1: (m >= 75 ? 3: 2),
                    Range = m < 50 ? "< 50": (m >= 75 ? ">= 75" : "50 - 75"),
                    Marks = m})
              .GroupBy (r => r.Range).Select (r => new {
                    RangeNo=r.First ().No,
                    Range = r.Key,
                    Count=r.Count(),
                    Avg = r.Average (x => x.Marks)})
              .OrderBy (r => r.RangeNo)
              .ToList();
    Console.WriteLine ("{0,-10}{1,-10}{2,10}{3,10:N2}",
            "RangeNo","Range","Count","Avg");

    foreach (var item in marksRange)
    {
        Console.WriteLine ("{0,-10}{1,-10}{2,10}{3,10:N2}",
            item.RangeNo, item.Range, item.Count, item.Avg);
    }
}
//Output
//RangeNo   Range          Count       Avg
//1         < 50               3     40.00
//2         50 - 75           10     63.30
//3         >= 75              5     85.60

In the above example the marks are arranged in to Ranges by Select method which returns a IEnumerable collection, on this the GroupBy method is used to group the Ranges and count the No. of students in that range, which again returns an IEnumerable collection, then on this OrderBy is used which again returns IEnumerable collection, on this ToList method is used to return finally a List as desired. Without extension methods if the above code is written using the static methods in conventional way it will be clumsy and the logic will be difficult to understand.