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

Let the side of the original cube = $$a$$

Volume of the original cube = $$a^3$$

The side of the resulting cube when decreased by 25% = $$\frac{75}{100}\times a=\frac{3}{4}a$$

Volume of the resulting cube = $$\left(\frac{3}{4}a\right)^3=\frac{27}{64}a^3$$

$$\therefore\ $$Ratio of the volumes of the original cube and the resulting cube = $$a^3:\frac{27}{64}a^3=1:\frac{27}{64}=64:27$$

Hence, the correct answer is Option B