Conversion of top 30-40 Bschools would be really difficult for you because they do have a 5-10% weightage for past academics. Although if you have a very good percentile in cat or other management exam that you are going for and by good I mean 99+ with some extra-curriculars you can still secure a very good college. Generally if you get a call from a good bschool you will be required to justify for your shortcomings in the interview. And if you can do that very well with whatever reasons you have or you can cook for, you can definitely convert a good Bschool. 

Some good options like SIMSREE, GIM and many more are always open for students who can score well in the exam but have average past acads.

So right now focus on how much you can score, rather than worrying about what you cannot change.

All the best.

SMIT-IIM-AMRITSAR-PGP/04

Well It all depends On which College for Which you are applying, colleges have different weightage for class12th Percentage and Different criterion To give Points to Your class12th Weightage so We can not deny the fact that You have lot of colleges which does have few weightage to class12th Percentage and more to percentile in Competitive exams So Don't loose Hope find such Institute and apply for that For the time being Just focus on Your percentiles.