You don't say which year the car is - there were two gearboxes fitted to the XC90 (assuming you have a diesel). From the errors I'm guessing it's a older pre 2006 MY 163 BHP car with a 5-speed gearbox (black engine cover).
In any case, this sounds like a typical problem of a worn gearbox unfortunately, it might be worth replacing the vehicle speed sensor which is easy to do as it's on the outside of the gearbox.
There are two speed sensors on the gearbox, and input speed (which is not necessarily engine speed as it is post torque converter) and output speed (road speed). The computer compares the two with what it expects and logs errors if it thinks there's a problem. It maybe that a locking clutch is worn in the gearbox which is causing internal slip and hence throwing up the error.
I would get a second hand sensor from e-bay and try it - it's a slim chance but could save you a lot of money.
You could also set fire to the replacement car that the sh**head who sold it to you has bought since he clearly would have known about the problem.
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2011 XC90 D5 Executive
2003 C70 T5 GT
2012 Ford Ranger XL SC
1977 Triumph Spitfire 1500
1976 Massey Ferguson 135
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