I own Redmi Note 3 since last one year. Totally amazed with the feature provided by the phone at this rate.

Now coming to your question, I was having the same issue from last 10-15 days. My phone was taking too much time for charging.  Even I was using the original MI charger and USB cable, but the problem was there.

Instead of going to the service center, I tried to change the USB cable. I used cable provided by MI from one of my friend and it worked.

So, I ordered a MI USB cable from there official website. Got delivered in time and now it is working properly. 

Earlier, I found the same problem with my Redmi 2 Prime within a year, I changed the cable then too and that worked.

So, I think the issue is with the USB Cable, order online one for you from mi.com, available at just Rs. 199 and if you are not using Original charger with 2A  output, this combo is available there too.

Hope, it will help you.

If you have any query, feel free to ask, I would to happy to help.

Thanks, 

GauRAv Sachan