The weight of an astronout is 60kg on earth, find the wight of the same object on the planet where the gravitational attraction has been reduced to 1/10 of the earths pull

The astronaut's weight is not 60 kg anywhere, because kg is a unit of mass, not weight.

If the astronaut's mass is 60 kg, then his weight is (60 kg) x (acceleration of gravity).

That's 588 Newtons on Earth, and 58.8 Newtons on a planet with 1/10 Earth's gravity.

The astronaut's mass of 60 kg goes with her, and doesn't depend on where she is.