Ages given in any document can easily be incorrect and care must be taken when using an age to infer a year or date of birth for an ancestor. That said, it still is important to remember what an age on a given date means–the age as of that date. If Elizabeth’s age is listed as fifty years on 6 August 1832, then at the youngest, she had just turned fifty on that date. At the oldest, she was one day shy of her 51st birthday. So Elizabeth could have been born on 6 August 1782 (if she had just turned 50) or as early as 7 August 1781.
Of course, this potential range of birthdates makes the assumption that Elizabeth knew when she was born, that she actually reported the age herself and gave her true age, and that the age has been transcribed correctly from the record. Any birth date, or range of birth dates, calculated from an age should be clearly sourced and noted in your records. Keep in mind that many times such ages will potentially conflict with one another and often with sources providing primary information about the event.