In reply to womblesi:
> I am planning on doing a 4 x 25m multi pitch route, to get off the guide says a that two 60m abseils are required. I was planning on climbing the route on a 70m rope but taking a 50m half rope with me.
>
> My idea is to join the two ropes with a double over hand knot then descend 10m ab over the knot before completing the rest of the descent to the belay station.
Everyone is saying you shouldn't have a problem. Maybe not, but sure wouldn't want to bet on it. If the ropes run unevenly, which is certainly possible even though their diameters are close, then the knot could be pulled back up to the anchor, in which case your thin rope will be 20m shorter than your thick rope. It is very hard to notice uneven running of the ropes while rappelling. You could end up rapping off the thin rope and end up hanging on the thick rope, supported by the knot wedged against the rings at the anchor. I know personally of two instances, one fatal, in which such a knot has pulled through the rings.
At the very least, you have to have knots in the ends of your ropes so you can't rap off them. It is conceivable, if the ropes are uneven, that you could let the shorter rope's knot jam up against the rap device and continue rappelling, letting the device pull the shorter rope down and thereby even out the ropes. I wouldn't want to count on this working without multiple experiments in a safe environment first.
Something you can do to mitigate uneven slippage is to feed the rappel lines into the device hand-over-hand, rather than just letting them slip through your hand.
You haven't addressed passing the knot on rappel. There are a range of ways to to this, from extremely simple with virtually no extra gear to absurdly complicated with ascenders, aiders, and multiple steps. You will certainly want to have that process dialed before having to use it anywhere consequential.
If I had to do something like this, here's what I'd do. I'd clip a quickdraw between the ropes so that they can't slip for the first person down. (The second person down better remember to undo this or you're screwed!) Once the first person is down and off rappel, they anchor the thin rope so that it can't be pulled up by differential running.