Question

            XDocument doc = XDocument.Parse(_data)
           XElement root = new XElement("student");
           doc.Element("marks").Add(root);
             doc.Save(_data)

the _data is the deserialized string xml and student is the root tag want to add
doc.save throws the error.How to save the root tag ?

the string xml

             <marks>
           <name>Martin</name> 
           <date>3/24/2012</date> 
           <field>Percent</name> 
           <new>33.3</new> 
           <old>10</old> 
            </marks> 

this is the string xml before root tag is added, once it is added it should look like
after the root tag is added it should look like

             <student>
            <marks>
           <name>Martin</name> 
           <date>3/24/2012</date> 
           <field>Percent</name> 
           <new>33.3</new> 
           <old>10</old> 
            </marks> 
            </student>

Answer 1

XDocument.Parse(_data)

implies that _data is XML, ie "<tag> <sub /> </tag>"

doc.Save(_data)

Requires _data to be a valid filename. Like "output.xml"

Ok, seems that you need:

//doc.Save(_data)
_data = doc.ToString();

Take 3:

You need to add the existing xml to <Student>, not the other way around.

//untested    
XElement doc = XElement.Parse(_data);  // not XDoc
XElement root = new XElement("student", doc);
//doc.Save(_data)
_data = root.ToString();