After many months in India I stumbled on my preferred method:

 * say nothing
 * give the [palms together Indian greeting][1] to the person asking (they will almost always respond in kind)

[![Photo by Saptarshi Biswas. licence: https://creativecommons.org/licenses/by/2.0/deed.en][2]][2]

 * continue with what I was doing

I do like that this is a bit more respectful to the other person.  However, the main advantage is that **when I just ignored the person begging they would often continue following me and asking** and every time I tried the above method they always moved on.  Works like magic.


  [1]: https://en.wikipedia.org/wiki/Namaste
  [2]: https://i.sstatic.net/F3AzF.jpg