I know very little about Asian languages, but this example from Europe may help you.
Latin is the apparent base language in much of Europe, although the ancient Romans borrowed many words from Greek. As the Roman Empire expanded, the Latin language was spread throughout most of Europe. It merged with the indigenous languages to produce French, Spanish, Italian, and Romanian.
Meanwhile, in northern Europe, Germanic languages remained dominant with several variations. The British originally spoke variations of German until the Romans conquered Britain. Latin creeped into their languages. The Norman Conquest brought French to Britain and within about three centuries, the Germanic, French, and Latin languages merged to form Old English. Languages constantly evolve so that most of us can read few words of Old English. However, if you look up the etymology of English words, you'll find the majority of our short words come from ancient Germanic words while our longer words come from Latin and/or Greek. Of course we've also borrowed a few words from many other world languages, such as American Indian tongues, Spanish, French, and Arabic.
Sanskrit and Chinese are two of the languages that spread through southern Asia in ancient times, merging with native languages -- and of course, always changing.