How to update value in json object with key as argument (using `jq`)

Using jq I want to update a value in a json object.The key of the value to be updated is passed as an argument.

Input

{"a": 1,"b": 2,"c": 3}

Expected output with argument: key=b

{"a": 1,"b": 42,"c": 3}

I tried to do:

jq --arg key b '.($key) |= . + 40'jq --arg key b '".\($key)" |= . + 40'

Both attempts result in errors:

• syntax error, unexpected '('
• Invalid path expression with result ".b"

How can I solve this problem?