A bowl contains raspberries and blueberries. Natacha added \(10\) more raspberries to the bowl, then determined that \(\frac{3}{10}\) of the berries in the bowl were raspberries. Jing then added \(20\) more blueberries to the bowl, then determined that \(\frac{1}{4}\) of the berries in the bowl were raspberries.
What fraction of the original berries in the bowl were raspberries?