I've had my Nexus 10 for a while and it's been great until recently and the battery now won't hold a charge. Whenever I unplug the charger it just turns off right away and when I plug in the charger that goes from 0 percent to a hundred percent in like 5 seconds
It may be because it came out on an earlier android version, requiring less power and battery to run. If you have a newer android version, e.g KitKat or Lollipop, it may be more intensive both visually and in terms of the power required to run it. Battery Doctor is a good application, (available on the play store), which might solve you issue.