If a rocket travels to Pluto and back, how much would the earth age?
That is totally dependent upon the speed of the rocket.
The most recent trip to mars by the New Horizons satellite took about 9.5 years so it would take 19 years round trip, earth time.
Now if you place a human inside that rocket things change because of Einstein's theory of special relativity. Because of this that astronaut would observe a slightly slowed down time. But the distance, time, and speed are not great enough for the human to be much more than a few minutes or so younger than had he stayed on Earth.