Two nationalized exams on same date as one exam postponed by IBPS

Respected Sir/Maam, As you might be aware most of the banks nowadays conduct exams individually for recruitment purposes. Currently Syndicate Bank is going to conduct one such exam. The notification which they published had date of exam mentioned as 19-02-2018, managed by IBPS. But due to some elections in one of the Southern states, they changed the date to 25-02-2018. Now here lies my problem, on 25-02-2018, AFCAT, an exam for recruitment in the Indian Air Force is going to be held, and as a graduate, i am eligible to apply in both. And when i got admit cards of both the exams, both of them have same time as well, forcing me to choose one. Now I have e-mailed regarding same to IBPS and Syndicate Bank, but IBPS is not cooperating while Syndicate's HR department has not replied. Now as an unemployed, i want to grab both opportunities to apply, and have paid examination fees as well for both, so I feel like my fundamental rights are breached. Please guide me as to what I can do in this