One thing to keep in mind about a k-bike is that they're like women; they need lots of TLC, but if you give it, they treat you well and it's worth it. If you want something that's low-maintenance that you can just get running and not have to touch for years, you might want to look elsewhere.
Fortunately, you're looking at an 87. I have an 85 k100RT, "First Year K" (FYK), or often sarcastically called "Finest Year K". Lots of bugs. But they worked out a lot of them by 87.
You're going to want to check the drive shaft splines. This involves separating the final drive from the swing arm. If these are dry or the splines look flat, that's a bad sign. This is a regular maintenance item on these bikes to grease the splines. I do it every 1-2 years. Some do it every year, others say as infrequently as every other tire change.
You can count on the mileage being wrong. These bikes are notorious for speedometer issues that result in lots of unrecorded miles. I've owned mine for at least 3 years and still don't have the speedometer working reliably yet. That having been said, I wouldn't worry about the mileage, as the engine is solid and will easily last hundreds of thousands of miles.
Other things to keep in mind when buying a k-bike. They're hot. Hot air from the radiator heats up the fuel tank and your legs. I converted mine to a naked bike, which helped, and also put new insulation on the underside of the fuel tank. It's not bad at all now. If it has the stock rear shock, it's crap; you'll want a new one. Oh, and the vibration! I almost forgot. It vibrates. It's better or worse at certain RPM's, so you'll learn what speeds you like to stay at. Fortunately, this one's an LT, so it has the most vibration insulation of any trim. Still, you may find yourself doing various mods to better secure fairing pieces, etc. Oh, and change the brake fluid every year. I didn't at first, then it started squeeling like a pre-teen girl at a Bieber concert. When I changed the fluid, it was brown! Most people never change their brake fluid, but in this case, it is necessary.
It was actually hard to think of bad things about k-bikes. Despite all that, they're reliable, they handle well, I love the ergonomics, and it's just fun to ride. Starts right away every time. Despite being a large-ish touring bike, the way the engine is mounted makes for a low center of gravity and sporty handling. Best of both worlds. I have all the luggage options too which is awesome for road trips. Plenty of power too; I've accidentally lifted my front wheel off the ground on take-off more than a few times :D
But probably the first thing I would do, if it were me, is ask why the fuel tank is missing. Seems odd to take a fuel tank off a running bike and never replace it. And if he knew that's all it needed, why not get another tank, put it on, and get a lot more money for it? Sounds fishy. Also keep in mind that the fuel pump, filter, and level sensor are inside the fuel tank, so those are probably missing too. That may be an additional expense to consider.
