This is a difficult question to answer. Much depends on the VA regional office for your area. On average, 6 to 8 months seems to be the normal approval time at the moment. Some approvals come through in as little as 6 weeks, but these are the exception. We know of people still waiting for an approval 12 months from the date of filing.
Keep in mind that if the benefit is approved, it is applied retroactively to the date of application. Also, if the applicant is over 90 years old, include a letter requesting that the application be expedited. The VA is supposed to give priority to any application for benefits by a veteran age 90 or older.