The earth is four times the size of the moon and the acceleration due to gravity on the earth is 80 times that on the moon. The ratio of the mass of the moon to that of the earth is?

NOTE: Firstly, it should be noted that the mass, as well as the weight of a body, is independent of its size.
∴ Let the weight of the moon = M_m x g_m
weight of the earth = M_e x g_e
But g_e = 80g_m
∴ weight of the earth = M_e x 80g_m
=> weight of the moon / weight of the earth = M_m x g_m / M_e x 80g_m
thus ^M_m/_Me ∝ ^g_m/_80gm ∝ ¹/₈₀
=> M_m:M_e ∝ 1:80