Again----"same time" is meaningless. Sure---do them the same week if you manage it---sending them at the same time is not relevant. One (2021 1040X) can be e-filed and one (2020 1040) can only be filed by mail. The amended 2021 return will likely take months to be processed. It is currently taking the IRS about six months or more to process amended returns. And your mailed 2020 return is going to take quite a long time as well. Mailed returns take months to be processed. Do not expect quick results from either one of those returns. When you mail the 2020 return use a mailing service like certified mail so you will know it was received. You will never see information about the 2020 return on the IRS refund site. That site only shows information for 2021 returns.
And when you send in the amended 2021 return you will need to watch for information here:
https://www.irs.gov/Filing/Individuals/Amended-Returns-(Form-1040-X)/Wheres-My-Amended-Return-1
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
