IIM

A candidate who scores just 20 on the percentile scale in CAT, hence, will find it difficult to get admission for MBA programs to any top part of the elite business schools, for all these institutes have put a very high cut-off percentage on a general basis in the range of 85 to 99 percentiles.

This very high cut-off range for all potential candidates includes even new and baby IIMs. All of them set the bar high even for the reserved categories. But then there remain some options for you.

A few private business schools and deemed universities offer admissions at the lower-end CAT score or even conduct their entrance tests. Many such institutes are Amity University, Lovely Professional University (LPU), and many others that assign those low percentiles additional weightage on other selection criteria, like their academic performance, group discussions, and personal interviews. Furthermore, there are some state universities or tier 2 and tier 3 MBA colleges that offer admission on a no-CAT basis. 

It all depends upon which IIM you get shortlisted, but considering your percentile in CAT 2023 that is 70, a very good chance stands by your side if the cutoff will be met by you in terms of that IIM.
For example, IIM Ahmedabad will set the minimum overall cutoff at 60 percentile for ST candidates while others may be different. Normally, top IIMs such as IIM Ahmedabad, Bangalore, and Calcutta are higher with cut-off values generally more than 90 percentile in most of the cases but relax it for the reserved categories.
Although your score may suffice for admission into some IIMs, admission is not guaranteed and will depend on your overall profile, including academic performance and performance in subsequent rounds like interviews.

According to the general guidelines laid down by most Indian Institutes of Management (IIMs), hostel fees are not included in the base fee structure. The fee structure includes mainly tuition fees, academic resources, and other essential expenses; hostel accommodation and all related charges are extra.

Fees for the hostel vary from IIM to IIM depending on the type of accommodation-single or shared room.

Some IIMs provide accommodations within campus limits at different rates, depending on the kind of rooms or facilities, but others have additional, separate charges for food; security deposits; and all other utilities.

Hence, check the specified fee structure of the particular IIM for exact details as hostel charges are included within the overall fee package by some IIMs and provided separately by others. Hence, while calculating the overall expenses for your course in IIM, you also have to consider the overall cost of living that includes hostel, food, as well as personal expenses to arrive at the total estimate.