what is the ratio of the volume of the new sphere to the first sphere.?

If $r$ is the radius of the first sphere then its volume is $\dfrac{4}{3} \pi r^3$ . If $d_2$ is the diameter of the new sphere, then

$d_2=2r-0.4(2r)=1.2r$

So the radius of the second sphere is $\dfrac{1.2r}{2}=0.6r$ and its volume is $\dfrac{4}{3}\pi (0.6r)^3=\dfrac{4}{3}\pi r^3(0.216)$

The ratio of their volumes is

$\dfrac{\dfrac{4}{3}\pi r^3(0.216)}{\dfrac{4}{3} \pi r^3}=0.216=\dfrac{27}{125}$

So the desired answer is $27+125=\boxed{152}$