For languages that have been around for a while, how close are ancient texts to the modern form of the language?

Can a person from Greece make sense of Plato and Sophocles in the original? Can someone from China read something written by Confucius? I am assuming that the original writings are still around. Hindi and Persian have also been around for a long time in written form and I am guessing maybe Korean, Japanese and possibly some other Asian languages.

It is hard to use English as an example. The language kept changing radically until fairly recently. The language of Chaucer is barely recognizable as English. We can read Shakespeare with a little effort. The writing from the eigthteenth century onward is pretty close to its modern form.