How much time is needed to prepare for the IIM Indore entrance exam, i.e., IPM?

There is no need to prepare for IPMAT separately if you have studied Maths up to class 12. Just revise all concepts and formulas time and again. If you are worried about English, it should be pretty easy for you considering you read and write in it regularly.

You should be disciplined and have a plan of action. You will be able to complete the entire syllabus required for the exam within 30 to 40 days.

After that, think of focusing your attention on topics that are essential for students. For example, my sister was not fluent in her language skills and she was not on the same level as her peers. For this, she spent extra time working on developing those skills. She completed her language section and devoted the rest of her time to mathematics and solving sums.

You should definitely look at time management and seeing where you lack. Being a student from a mathematics background, you will not need private classes or even tutoring. Prepare well and in advance to go back and work on your weaknesses.