If you are applying for a personal loan through a traditional bank, approval can take days together. However, if you are applying for personal loans online (like here) then you can get approvals in minutes and even the money disbursed in less than hours. Thanks to modern technology!
The whole processing of approving your application involves an underwriting process where the bank checks your credentials and credit worthyness. This is the most time consuming process. Traditional banks have approval heirarchy (bank managers, seniors etc). However in online applications, these hurdles are taken away and you're able to do the whole underwriting process easily with the help of technology.
In India, about 72 hours is the shortest time taken to approve and disburse a loan amount on online aplication.