Management Aptitude Test Dec 2019 Paper

Let the edge of each smaller cube be $\mathit{x}\mathrm{m}$.
Then, volume of each smaller cube $=\left({\mathit{x}}^3\right){\mathrm{m}}^3$.
Volume of 8 smaller cubes $=\left(8{\mathit{x}}^3\right){\mathrm{m}}^3$.
Volume of 8 smaller cubes $=$ Volume of the original cube.
$\Rightarrow 8{\mathit{x}}^3=72\Rightarrow {\mathit{x}}^3=9$ $\Rightarrow \mathit{x}=\sqrt[3]{9}\mathrm{m}$
Thus, the edge of a smaller cube $=\sqrt[3]{9}\mathrm{m}$.
The edge of the original cube $=\left(\sqrt[3]{72}\right)\mathrm{m}=\left(2\times \sqrt[3]{9}\right)\mathrm{m}$
∴ Required ratio $=\sqrt[3]{9}:2\times \sqrt[3]{9}=1:2$