Let the net gravitational force on the rocket due to earth and moon is zero when the rocket is at a distance x from the moon.
Also let mass of moon be M, then mass of earth will be 81M.
Now the gravitational force due to earth and moon will be equal on the rocket at the point where net force is zero
So applying Newton'* law of gravitational we get
GMm/x^2=G81Mm/(r-x)^2
=> 9x=r-x
=>x=r/10
