The weight of a cube varies directly as the product of its volume and its density. The ratio of densities of the materials of the first cube and second cube is 27:16. If the weight of the first cube is 4 times the weight of the second cube, then what is the ratio of the edges of the first cube and second cube?

The weight of a cube varies directly as the product of its volume and density.

The ratio of densities of the materials of the first and second cubes is 27:16

The weight of the first cube is 4 times the weight of the second cube.

Weight is directly proportional to density.

​$$\frac{W}{D} = Constant\\\ \\\frac{W_1}{W_2 } = \frac{D_1}{D_2} × \frac{V_1}{V_2} \\\ \\\frac{4W_2}{W_2 } = \frac{27}{16} × \frac{V_1}{V_2}\\\ \\\frac{64}{27} = \frac{a_1^3}{a_2^3}\:(V_1=a_1^3,V_2=a_2^3)\\\ \\\frac{a_1}{a_2} = \frac{4}{3}$$   

Thus, correct option is (d).