jquery sum of multiple input fields if same class in one input

I think your issue is here:

$("#destination").val(sum);

change it to:

$(".total").val(sum);

And instead of change event i suggest you to use keyup instead.

$(document).on("keyup"

You pretty much had it, just needed to adjust your JQuery a little bit for the appropriate selectors

updated fiddle : http://jsfiddle.net/5gsBV/7/

$(document).on("change", ".qty1", function() {
    var sum = 0;
    $(".qty1").each(function(){
        sum += +$(this).val();
    });
    $(".total").val(sum);
});

I suggest this solution:

html

<input type="text" class="qty1" value="" />
    <input type="text" class="qty1" value="" />
    <input type="text" class="qty1" value="" />
    <input type="text" class="qty1" value="" />
    <input type="text" class="qty1" value="" />
    <input type="text" class="qty1" value="" />

    <input type="text" class="total" value="" />

<div id="result"></div>

js

$(".qty1").on("blur", function(){
    var sum=0;
    $(".qty1").each(function(){
        if($(this).val() !== "")
          sum += parseInt($(this).val(), 10);   
    });

    $("#result").html(sum);
});

fiddle

$(document).on("keyup", ".qty1", function() {
    var sum = 0;
    $(".qty1").each(function(){
        sum += +$(this).val();
    });
    $(".total").val(sum);
});