Your code is fine but i re wrote it to suit your needs. I hope this is what you were looking for. Basically you need to impliment the "else if" statement.
HTML Code:
// First hide the platform options
$("#platform_option").hide();
// now toggle if checked, but first assign click to the checkboxes
#("#joomla,#wordpress").click(function() {
if($("#joomla").attr("checked")==true) {
$("#platform_option").show('slow');
} else if($("#wordpress").attr("checked")==true) {
$("#platform_option").show('slow');
} else {
$("#platform_option").hide('slow');
}
});
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