You can start an online business with as little as 20k, examples –
Write a Book
Start a consultancy
Start a service based company example-
Small business example : Online cup cake store, Home made chocolates, Hand made Candles, Hand made Perfumes and soaps, Handicrafts etc. To begin with,
Research, Research and Research!
Research does not costs you money, thanks to Google! Once you laid your foundation, and done enough research, get your ideas jotted down, research the market, test your idea with friends and family. Your groundwork is the foundation, it must be robust. It might take a few months for you to complete your market study and analysis. After which you can invest the 20k in development of your website.
There are online website builders, where you can get a suitable template and make the website yourself which should not cost you much, or you can get it developed by a freelancer.
Here is the article from Yourstory to help you with other business ideas within 10k
Here is the link of available website builders to help you.
10 Best Website Builders Reviewed. (I bought and signed up.)