I was working in ITPL Whitefield for 2009-2011. The rent was 8k for the first year, 11k for second and 14k for the third. That's the way most of the landlords charge. Though I was a bachelor and lavish spending was rare, I hardly had any money to save or send back to family. You will get frustrated by the daily traffic problems, pollution, unavailability of clean drinking water (had to buy those big bottles every two days). If you plan to travel to your hometown once every six months or so, that would add to additional expenses- getting leaves, flight or train tickets all will add to the hassle.
Getting a proper house within your budget would also be a problem. If it isn't a furnished one, you need to buy all the stuff from furniture to appliances.
As you have said you are the sole bread-winner, living within the budget might get problematic. From the 9L, you have to spent at least 15k per month or 1.8L towards rent. 50k minimum for food and office commute. If you add shopping, grocery, travels, medical and other miscellaneous expenses, you are left with nothing to save.
There is nothing great to do in Bangalore city during the weekends apart from movies and malls. And it is not the same old cool and serene place that it used to be. Summers are too hot now.
I would suggest to wait for a year and try for better offers above 10L in Kolkata or even bangalore. You might miss your home and the awesome food of WB. I have moved to my native in Trivandrum, and trust me, nothing feels like home
BTW, loved your travelogues. Planning to visit Sikkim sometime this year.
Thank you for your detailed reply
Thank you everyone, for your help. Though I haven't yet decided anything yet, but I'll surely let you know you guys.