I appreciate that this posting is probably far too late but a completely different slant may be of interest to others ....
No matter what the purchasing percentages, if I were you, it would be my home we are talking about and I would not be happy if someone I jointly bought a property with simply decided they wanted to rent their share to what would effectively be a stranger to me. How do you know you can get on with this new person. What happens if they never wash a dish or clean the floor ? After all, unlike the co-purchaser, a tenant has no financial interest in the property and has no incentive to keep it up as 20 years letting experience tells me is the case with 99% of tenants, so you may be taking on much more cleaning or accepting a dirtier environment as well as running repairs. Who is responsible for "managing" them and if it comes to a situation where you cannot stand them of fall out and they leave, will the co-purchaser expect you to pay the rent for "losing" her tenant or pay her mortgage in compensation ?? It seems fraught with potential problems.
It all sounds a bit much to me and I would simply refuse unless I could choose, manage and have full control over the tenant as a resident landlord so they can be kicked out immediately if they cause a problem and from their rent I would pay the co-purchasers share of mortgage, rates, insurance and all other shared costs first, then expect to keep any balance for my trouble. I would equally expect the co-purchaser to make good any shortfall if the tenant should be late paying, cause any damage etc., and pay for all costs associated with finding a replacement. If she wouldn't agree to this I would simply refuse and a sale would be the only option. Any letting of a room is going to change the status quo and the big question is "Why should you have to accept this if it is likely to be to your detriment ?". Forget the money and who gets what, your sanity and quality of life are the most important issues to my mind.
Sorry if this is not particularly helpful, but that is my view.