OP, I would suggest you buy a MTB.
MTBs have thicker tires, better suspension, and are marginally heavier and stronger - than hybrids. Given your prime usage will be for workouts, and you intend to do some off-road rides - MTB will definitely be a better option.
Thicker (knobby) tires (2.0") - more grip (better for off-road, and on Indian roads), marginally more traction (better for workouts - more pedaling effort required)
Front suspension - better for off-road, over footpath rides (if *you* intend to ride on footpaths during traffic jams, although I would not promote you to). Also, suspension consumes some of your pedaling effort marginally reducing the % tranfer of your pedaling effort to the drivetrain - this results in tougher rides compared to on no suspension.
If at all you start using it for commutes, long distances in particular, you can always buy a new set of semi-slick (1.0"/1.2"/1.5") tires for ~ Rs 1,000 a pair, and use them instead of knobby tires. That would turn your MTB to a hybrid, and make the rides considerably easier.
Additionally, some MTBs have lock-out mechanism on front suspension which enables one to lock the suspension and make it rigid - which also would make the rides easier.
That said, it is hard to find a decent basic MTB below Rs 20,000, thanks to the increase in import duty on cycles. Check Trek 3500, KHS Alite 150 - these should cost close to Rs 20,000. I am not updated with the current models in the market, so will do my bit of research and get back.
Given your limited budget it is better if you hunt for a good-well maintained-used-MTB, after all MTBs from brands such as Trek, Merida, KHS, Cannondale, Bergamont are made to last ages (if maintained well).
Check these online portal for used bikes classifieds -
link1 &
link2. It might help.
PS: I own a Merida Matts 20 MD, bought in Oct 2009, ~15,000 km run, still doing great.
Good luck, and happy cycling!