Drupal 7 how to save values to an Entity in Form Submit.

Yes you can add a field with a db_query like this

time_taken_updated = db_update('quiz_node_results')
 ->fields(array(
 'time_taken' => $time_taken ,
 ))
 ->condition('result_id', $result_id, '=')
 ->execute();

but it's better to do it with Entity_Metadata_wrapper in your hook_form_submit

like

$saq_results = entity_load('quiz_result', array($result_id));

$saq_results_wrapper = entity_metadata_wrapper('quiz_result', $saq_results);

$saq_results_wrapper->time_taken->set($time_taken);