Hi

Getting a call from a B- School depends upon a number of factors like  your percentile  score in CAT and academic profile i. e.percentage of marks obtained by you in  class 10th, 12th and graduation, work experience.
Your academic profile is good as per the details mentioned by you but 87.8 percentile in cat is not enough for getting into IIM even  for new /baby IIMs you should have good at least 90 percentile in cat

With your overall 87.8 percentile in CAT you have chances in following B schools which are listed below :-

*Indian Institute of Financial Management and Research, Changambakkam
*Xavier Institute of Management and Entrepreneurship, Bangalore
*Prin. L N Welingkar Institute of Management Development and Research, Mumbai
*Institute of Management Studies, Banaras Hindu University, Varanasi
*Sydenham Institute of Management Studies, Research and Entrepreneurship Education, Mumbai
*University Business School, Panjab University, Chandigarh
*Bharathidasan Institute of Management, Trichy
*FORE School of Management, New Delhi

For details you can checkout our page, the link for the same is provided below.

https://bschool.careers360.com/articles/what-if-my-cat-percentile-between-80-and-90-do-i-have-any-chance-at-top-b-schools

After getting a call , one has to go through WAT/GD/PI , and then he/she is finally selected for admission on the basis of performance in these rounds  , percentile score in CAT, academic profile and work experience.

To get the list of colleges that you can get call from  for your MBA, you can use CAT call predictor, the link for the same is provided below

https://bschool.careers360.com/pathfinder/cat

It will let you know the colleges from which you have chance to get a call  for  PGDM or MBA based on your category, your percentile score in CAT examination and your academic profile .

If you have any other doubt then feel free to ask them :) we are always here to help you out and guide you

Thank you