Do one need to pay tax for online side hustles? E.g. Selling online courses/subscription fees collected/sales of e-book?

You have to report it if you earn above a certain amount. But you may not have to pay tax.

If you earning above S$6000 a year, by the law, you will be required to file your taxes. More information can be found here: https://www.iras.gov.sg/media/docs/default-sour...

It's super grey.

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For example when you sell a used item on carousell for higher than purchase price, is that 'profit'?

By right, yes.