I applied for my UK tourist visa on 30th March and got an SMS saying my application has been sent to the embassy. I haven't heard anything since. Any idea how long they typically take for processing or the next update? Because there is no way to track it online.
The Home Office provides a tool (in beta version) to estimate the time your application will take. The announced duration is in business days.
For General Visit visas from New Delhi, 98% of applications take 10 business days or less. You should go through the estimation process with your specific situation (since I don't know your precise situation). But a priori that's not too bad you got no answer yet.
It has been only 4 business days so far, usually 5 applications in 6 are processed within this timeframe. Last Friday and today (Monday) were bank holidays in the UK so the embassy employees were not working. I didn't find if there is any Indian holiday, if so it would make the process even longer. Your application may take another 10 calendar days without it being abnormally long.