So I have a bike with a 1975 dt400 engine in a 1975 dt200 frame. I need to replace the rear sprocket and I have purchased a sprocket for both of the aformentioned models but neither fits the bolt pattern and I need some help with this.

Here is a picture of the hub where the sprocket attaches. As far as I can tell there are no markings on the hub its self or the wheel. 

EDIT: It is a 51 tooth sprocket and I have pictures of it down below.

Look inside the brake drum area or you may need to remove the "cush drive" from the hub.  Should be some sort of casting number on the hub.

Telling us exactly what wrong sprockets you bought would be helpful...  wouldn't be the first time that a seller sold wrong parts.

P.S.  No such thing as a 1975 DT200.  Did you mean DT250?  If so, pretty sure they would both take the same sprocket. 

 

Guessing DT250 typo? but wheel looks like the sprocket carrier is on its own bearing not sliding on the hub extension. I've got a TT250 wheel like that but brake plate is anchored to the arm by a slot although can see your brake plate isn't that type. Wonder if its something non yamaha after all that.
Found my early TT250 one & measures 80mm straight across. ID of sprocket as near as can line it up over the top looks 62mm. No help probably but there ya go. My sprocket carrier has a bearing in it normally plus a short collar that sits in the bearing & another collar that sits in the seal. But essentially sprocket carrier is separate from the hub, not sitting on a hub extension like your correct DT400 DT250 would have.
 

www.partzilla.com/catalog/yamaha/motorcy...80/tt250g/rear-wheel

So I finally got back around to the DT. I removed the rear wheel and attached I have a picture of the only casting mark on the hub. Also I measured the sprocket. The center hole is 90mm wide and from center to center on the bolt holes directly across from each other its 110mm if that shines any light. The casting mark reads '1 up top and 11 on the bottom.

Are you sure that's the only casting mark? Pretty sure that I can see characters in the segment two above the one in your photo.

Any numbers/letters might well id what model it fits, so important to show/list them all (they often get covered in crud).