This is hard to gauge, i got my PR in May and at that time the processing times had begun to creep up. They are much higher now. The funny part is i got an update and request in my profile and i thought it was PPR. I quiickly opened it and turned out that it was RCMP request. Mega bummer
Anyhow, I got RCMP request on a Monday afternoon. I had everything done at hamilton police center and they dispatched it the next day.
By next Tuesday (8 days in total) I had received the results in my mail which I promptly sent to the email address they had asked me. Then I didn't hear anything back. So on Monday I sent them an email to check. Within a few hours I had a ghost update which i called to check the other day and found out application was approved. However there was no PPR.
I went to my local Hamilton MP's office and they first called the immigration minister to confirm that my profile had been approved on 14th May but they were waiting to send me an appointment for interview and it may take up to 8 weeks. Then the kind lady at my MP's office called up the hamilton CIC office to check with her contact there. That got me the PPR and i had a date of 27th to interview at the hamilton office.
But without the MP intervention i don't think it would have been soon.