Basically, the time depends on your documents and your credit records. Suppose, if you have all the documents that required for this purpose like, voter card, pan card, identity proof, employment proof etc., all are genuine and error free, then you may get loan approval within a few days. But if you have some documents error, then you has rectified those documents first and then you should apply for car finance.
Another is, you credit record. If you have a good credit record then you may get an auto loan direct and easy. But if you have credit problems due to any reason like, unemployment problem, insolvency, divorce problem, repossession issues etc., then you may face lots of problem. The car lenders always avoid people those who have bad credit record because they thought that you are may be unable to pay the loan amount.
But there are some companies, who can assist you and help you to get the car finance though you have credit problems, Find them online. There are various car loan service providers who will first listen to your problem very carefully and then they will solve it.