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

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 :
$$\eqalign{ & = \frac{{1000}}{{421.875}} \cr & = \frac{{1000000}}{{421875}} \cr & = \frac{{64}}{{27}}\,Or\,64:27 \cr} $$