add a class to the textbox what you want to add, its for to select that control form JQuery, here I added a class name
addition
<div class="form-group col-md-4">
<label>Sick Leaves Allowed : </label>
<asp:TextBox ID="txt_sick_leaves" runat="server" CssClass='form-control addition' ClientIDMode="Static"
placeholder="Number Of Sick Leaves Allowed"></asp:TextBox>
</div>
<div class="form-group col-md-4">
<label>Casual Leaves Allowed : </label>
<asp:TextBox ID="txt_casual_leaves" runat="server" CssClass='form-control addition' ClientIDMode="Static"
placeholder="Number Of Casual Leaves Allowed"></asp:TextBox>
</div>
<div class="form-group col-md-4">
<label>Total Leaves Allowed : </label>
<asp:TextBox ID="txt_total_leaves" runat="server" CssClass='form-control' placeholder="Total Leaves Allow" ClientIDMode="Static"></asp:TextBox>
</div>
From Jquery select by class name and add values and display in result textbox
$(document).ready(function () {
$(".addition").change(function(){
var value1=$('#txt_sick_leaves').val()==''?0:parseInt($('#txt_sick_leaves').val());
var value2=$('#txt_casual_leaves').val()==''?0:parseInt($('#txt_casual_leaves').val());
var sum=value1+value2;
$('#txt_total_leaves').val(sum);
});
});
JSFiddle[
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