jmc

Let the original measure of the arc be $x^{\circ }$ and the original radius have length $r$, so the original arc has length $$\frac{x^{\circ }}{360^{\circ }}\cdot 2\pi r.$$

The new measure of the arc is $\frac{6}{5}{x}^{\circ }$ and the new radius is $\frac{5}{4}r$ so the new arc has length $$\frac{\frac{6}{5}{x}^{\circ }}{360^{\circ }}\cdot 2\pi \frac{5}{4}r=\left(\frac{6}{5}\cdot \frac{5}{4}\right)\left(\frac{x^{\circ }}{360^{\circ }}\cdot 2\pi r\right)=\frac{6}{4}\left(\frac{x^{\circ }}{360^{\circ }}\cdot 2\pi r\right),$$ which is $\frac{6}{4}$ the length of the original arc. Hence the arc length increases by $\boxed{50}$ percent.