"no one answered" is correct and usable in written English. You can use it whenever you are looking to express that nobody provided a response to an inquiry or statement. For example, "I called out for help, but no one answered.".
No one answered the door on Tuesday afternoon.
Initially when we knocked on her door, no one answered.
No one answered the door there on Wednesday.
No one answered calls placed there on Thursday evening.
No one answered the phone at the course on Wednesday.
No one answered the door at his home on Friday.
No one answered calls placed to the company on Saturday.
When I feel like I can't trust my brain 100%, Ludwig really comes in handy. It makes me translate and proofread faster and my output more reliable.
Claudia Letizia
Head Translator and Proofreader @ organictranslations.eu