SOLUTION :
The sum of the volumes of three cubes $=(20)^{3}+(16)^{3}+(12)^{3}$
$=8000+4096+1728$
$=13824 \mathrm{~cm}^{3}$
$\therefore$ Edge of the new cube
$\begin{array}{l}=\sqrt[3]{13824} \\=24 \mathrm{~cm} ; \text { Ans. }\end{array}$
$\therefore$ Correct option is (C).