Is this wide spread? Are there celebration both days, is this common among both sexes. Why is this so?
I haven't heard of this. We celebrate birthdays only once in a year, like everyone else! :)
When you click through to one of the links in the article, it explains that parents sometimes alter their kids' birthdays, though after having read the blog post a couple of times, it's still not completely clear to me why they do so. Here's the actual source blog post...
http://chamatkarindia.blogspot.in/2012/01/happy-birthdays.html
It's hard to tell how common this is. It's certainly not talked about much, at least not in the circles that I move around in.
I have heard stories like this before though. It usually has something to do with the nature of the academic year. Most Indian schools run for 10 months from June to March (April and May being summer holidays) and children begin kindergarten when they're four (sometimes five).
In some schools, parents with children whose fourth birthday lies in the later months of the academic year (such as December, January or February) are often told to wait for an additional year before seeking admission. In such cases, parents who want to avoid waiting for a year will quote an earlier date of birth at the time of admission.
Not all cases may be motivated by such reasons though - I've heard rumours (only rumours, mind you) of students whose year of birth is pushed forward (say from 1995 to 1998) so that they can begin schooling at a more mature age or so that they can play in sports teams that have age restrictions imposed on them.
All in all though, I'd say such extreme alterations of birth-years are rare and may often be nothing more than rumour. The birth-day alteration on the other hand, while certainly not a huge trend, may be much more common than most people believe.