The relative mass of a carbon atom is 12"gmol"^-1, or 12 grams per mole.
The question tells us this is 10% of the total mass of the molecule, so we can calculate this simply by
12"gmol"^-1 " * ((100%)/(10%)) = 12 * 10
= 120"gmol"^-1
This is the minimum mass of the compound, because if you have, say, a mass of 110"gmol"^-1 then carbon, which is 10% of the total, comes to only 11"gmol"^-1, though we know that carbon-12 has to come to 12"gmol"^-1, by the very definition of carbon-12.
This is only a minimum mass, though, because you could have, say, a mass of 240"gmol"^-1 in which case 24"gmol"^-1 of it is carbon, so you have 2 carbon atoms (24/12 = 2), even though the total carbon percentage is still 10%. So you can have more mass than 120"gmol"^-1, but not less.
