Since the query also mentions Jet Airways, I checked that Airlines' official website https://www.jetairways.com/EN/IN/Home.aspx/. There, too, the provision to select ticket booking for a senior citizen is very much there.
I checked out the same one-way flight as Air India, for Chennai to Bengaluru. Please see the attachment, wherein you can see there is 'Senior Citizen' option when you select the number of passengers. I selected that box. Then I selected a date for this month, but a message appeared on the screen that I can book for 14 days later only (not a recent, upcoming date). So, accordingly, I selected for next month, 6th October and the Economy Saver flight, with departure time at 8.20 a.m. The final fare showed as Rs.2,600/- for Economy Saver, 8.20a.m. flight October 6th. Without the concession (when not selecting senior citizen box) the fare showed as Rs.2,730/- for Economy Saver, same time and date.
In a similar manner, you could check out other flight carriers, compare prices and then accordingly book. Keep in mind your budget. Also, consider whether or not you would have a meal on the flight as you could find a flight fare which does not include the meal price and hence the fare would be less.
When you make a commitment, you create hope. When you keep a commitment you create trust! ~ John C. Maxwell