You have two different issues.
1st is that related to adv. of Teacher Eligibility test (Eligibility test)
and 2nd is with regard to adv. of job (recruitment Process)
Its seems that recruitment rules provides for lesser age but eligibility exam provides for larger age limit.
Accordingly, there is need to challenge the vires of order providing validity of age limit of Teacher eligibiilty test over and above as provided in recruitment rules. Its administrative mistake which needs to be rectified to avoid such situation.