It possibly may be that the seller knew of the problem but it doesn't necessarily make it expensive to fix.
Need to be methodical -
Check for charging voltage when engine is running - needs to be 14v and some. Be careful as an alternator on the way out may work some of the time but not reliably. Also check the alternator is cold an hr or so after stopping - if failing rectifiers are drawing a parasitic current that might keep the alternator warm until the battery is flat.
Check for parasitic drain - wait 10 mins after engine is fully off and measure current draw, it could just be a sticking switch leaving a bulb turned on overnight. Needs to be 0.05 amps or less (rule of thumb, xc90 could be a bit more or less).
Once you know the engine is charging the battery and nothing is discharging it overnight, start thinking about CEM and/or immobiliser issues and reading the codes must be the first step.
If you can localise the problem a bit you may get more useful responses from the forum.
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