Well if you look at the scores, about 25% of a year group passes the test. It's something like 16% of state school kids and 36% of independent schools. Unfortunately the guy who compiled these stats closed down his website, so it's not so easy for me to look up.
The variation is enormous though. My kid's school is boasting about 95% of their kids passing the test. I know they've been prepping the test because well, that's what the kid has been doing for past couple of years.
> if a child passes the 11+, the private lose all the potential senior school fees.
It's true that some schools try to discourage the kids from taking it for that reason, but of course that's only true if there's a senior school section.