Is a person with 15 years of study gap who is 35 years old eligible to pursue MBA now?

Any graduate with requisite percentage can apply for MBA after clearing aptitude tests such as CAT, MAT, CMAT, ATMA - AIMS, etc., as applicable to the institute of your study. Group Discussion and Personal interview are normally conducted by the institute. You may quote the reason for study gap, if

Yes Siya, you can pursue MBA as there is no age limit for pursuing MBA. If you have a work experience then you will need to show your work experience certificate but if you don't have work experience then you will need an affidavit mentioning the reason for your gap of 15 years.

There is no age limit for doing MBA, you can certainly do that. However, if you did not had any experience during last 15 years, you may not find a job easily. If you want to do it for learning, you should do a part time or full time MBA.