Each side of a cube is decreased by 25%. Find the ratio of the volume of the original cube and the resulting cube = ?

Answer: Option C

Let the side of cube = 10 cm
∴ Original volume = 10 × 10 × 10 = 1000 cm³
Now, side of new cube : = 10 - 25% of 10 = 7.5
∴ New volume = 7.5 × 7.5 × 7.5 = 421.875 cm³
∴ Required ratio :
$$\begin{array}{rl}& =\frac{1000}{421.875}\\ & =\frac{1000000}{421875}\\ & =\frac{64}{27}Or64:27\end{array}$$