In Sanskrit, small words (morphemes) are combined to form compound words through a process known as Sandhi. Sandhi splitting is the process of splitting a given compound word into its constituent morphemes. Although rules governing word splitting exists in the language, it is highly challenging to identify the location of the splits in a compound word. Though existing Sandhi splitting systems incorporate these pre-defined splitting rules, they have a low accuracy as the same compound word might be broken down in multiple ways to provide syntactically correct splits. In this research, we propose a novel deep learning architecture called Double Decoder RNN (DD-RNN), which (i) predicts the location of the split(s) with 95% accuracy, and (ii) predicts the constituent words (learning the Sandhi splitting rules) with 79.5% accuracy, outperforming the state-of-art by 20%. Additionally, we show the generalization capability of our deep learning model, by showing competitive results in the problem of Chinese word segmentation, as well.