smc

Let us say that the radius of a circle is $r$. When the radius is increased by $1$, the new radius is $r+1$ so the diameter is $2r+2$. We know that the circumference of a circle is $2\pi r$ so $2\cdot \pi \cdot (r+1)=\pi \cdot (2r+2)$. Finally, the problem asked for the ratio of the new circumference to the new diameter is $\frac{\pi \cdot (2r+2)}{2r+2}=\boxed{\pi }$.