I like the question you raise here. Similarly: we learned today that there were 160M iOS devices out there. What year were there 160M Windows machines?
In 1993, twelve years after the introduction of the IBM PC, there were 152 million personal computers [1]. That figure includes Macs, and many of the IBM PC compatibles were probably running only DOS or OS/2, not Windows.
I'm guesstimating that the Windows platform reached an installed base of 160m around 1996. That means it took iOS 1/5 of the time to get to 160m.