I agree with Daniel, you should base your offer on the current rent numbers.
With that being said.....
How long have the current tenants been in place? If for a long time, you should have a conversation with them about raising the rent. They most likely know they are getting a good deal, so you can ask them what they think is a reasonable rent increase. If they are involved in the rent increase conversation, they may not feel "alienated" by the new landlord. You can also talk about a scheduled rent increase. 1st year is $25/mo. 2nd year is another $25/mo and 3rd year is $25/mo. Or do $37/mo 1st year and $37/mo 2nd year. Now you're up to market rents and they don't feel like you hammered them with a big rent increase right away.
I also think you should have a reason to justify the rent increase to the tenant. Ask them what issues they are having with the property. Then tell the tenant "I'm going to increase the rent $25/mo (or $50/mo) but i'm going to improve that part of the property for you. Does that sound fair to you?". Makes the tenant feel like they are at least getting something for the rent increase.
My coworker bought a duplex in St. Bernard a few months ago with well below market rents and this is how he went about it. Worked very well for him.
