Hello Aspirant,
Rank in an exam is the position assigned to you among others who competed with you, based on the percentile you have scored .Percentile is a score based on how many people have scored below you . Now coming to merit number, imagine you applied to a university for a course along with 50 other applications, here you will be assigned a merit number according to your rank in comparison to those applicants. So a merit number is the number assigned to you on a merit list . Note that I have explained in general.
All the best
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