After studying my usage history, I have figured the problem. My total internet usage is 6GB (not 9GB as I was erroneously stating earlier). Of this, 2GB was covered in the limited download plan (since it started mid-month). For rest 4GB, I have been billed.
According to bill, my limited plan is effective from 3rd Dec. In the morning of 3rd Dec, I was not aware that plan change had become effective and my speeds at that time were also fast as per previous 1mbps unlimited plan. So I downloaded a lot of data. In the afternoon, I got a call from CC that my new limited plan has become effective and I should reboot the modem. My speeds then reduced and I was careful of my usage that moment onwards.
Apparently it is the large data that I downloaded in the morning, that has upset the balance.
I will try to explain this to Airtel CC when they call me. Guys, do you think I have a good case for defense?