What are my chances of getting into any of the old IIMs or XLRI with this profile: class 10 - 69.7%, class 12 - 83.8%, B.Com - 49.6%? I am a CA.

Your mentioned scores are very low and being a CA will only give you an advantage. IIMs give special preference to those who are CA or pursuing it. The main question is if you are eligible to write the CAT exam.

The criteria for writing CAT is to be a Graduate from a recognized University or a final year candidate in any discipline having a minimum of 50% marks. There are relaxations for those with a quota like SC/ST and they can have a minimum of 45% marks in graduation to write the CAT exam.

Not much weightage is given to academics at XLRI but they still need a minimum of 50% marks in UG. So, try to score well in XAT- anywhere from 95 to 96 percentile. This is because the higher you score the better chances you have. XLRI has no reservation policy and admission there is purely based on merit.