This question is really asking which solvent dissolves nail lacquer fast without much fuss. Let us go through the choices one at a time.
Option A, acetone: this is a small polar ketone molecule that is an excellent solvent for the nitrocellulose based resin used in nail polish. It breaks up the polymer film almost instantly and, being very volatile with a low boiling point near 56 degrees C, it flashes off the nail quickly. This matches every requirement of a nail polish remover, so it is the right pick.
Option B, benzene: even though benzene can dissolve some organic films, it is a proven carcinogen and toxic by skin contact and inhalation, so no cosmetic manufacturer uses it. Rule this one out on safety grounds alone.
Option C, petroleum ether: this is just a mixture of low boiling nonpolar alkanes. It is good for degreasing or extracting oils but it has very poor solubility for the polar nitrocellulose lacquer film, so it will not strip nail polish efficiently.
Option D, acetic acid: this is the acid found in vinegar. It is corrosive to skin in concentrated form and has no special power to dissolve a lacquer polymer, it works on ionic or basic stains, not on a resin film.
Since only acetone satisfies both the solvent power and the safety and volatility requirement, the correct choice is option A, acetone.