I can't get my head around how earthing the outer cylinder affects the potential difference between the plates. Also, if you positively charge the inner cylinder, then negative charge should accumulate on the inner side of the outer cylinder. So the outer side is at a positive potential. So shouldn't it mention which side of the cylinder we've earthed, because the charge flowing out should depend on that.
I've solved the problem, but I just need some physical intuition for the P.D between the plates (thank you photon for pointing that out).