“I am sorry I will not be able to join you guys for the movie. Siddharth has exams. I need to take his studies.” You can get away making a statement like this, practically anywhere in India. Not an eyebrow will be raised, no one would find anything unusual about what you said and whether or not this is how it is said, your message would have been conveyed.
Well, firstly, this sentence (I need to take his studies) is not grammatically correct and secondly, this is not how it is said. This can easily be another example of our mother tongue influencing the kind of English we speak. I am sure every Indian language has a typical way in which something like this is said, like in Marathi we say “अभ्यास (studies) घेणे (take).”
However, in English, studies cannot be given or taken. So the correct way to say this in English would be, “I am sorry I will not be able to join you guys for the movie. Siddharth has exams. I need to help him with his studies / I need to help him study.”