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.