In a Class X Board examination, ten papers are distributed over five Groups - PCB, Mathematics, Social Science, Vernacular and English. Each of the ten papers is evaluated out of 100. The final score of a student is calculated in the following manner. First, the Group Scores are obtained by averaging marks in the papers within the Group. The final score is the simple average of the Group Scores. The data for the top ten students are presented below. (Dipan's score in English Paper II has been intentionally removed in the table.)
Note: B or G against the name of a student respectively indicates whether the student is a boy or a girl.
Each of the ten students was allowed to improve his/her score in exactly one paper of choice with the objective of maximizing his /her final score. Everyone scored 100 in the paper in which he or she chose to improve. After that, the topper among the ten students was:
Lets first consider ayesha's marks , her 7 marks will increase in geography . So increase in her average marks is 7/(2*5)  = 0.7. So new average is 96.9 . </br>
Now for dipan , his 5 marks will increase in mathematics . So increase in his average 5/5 = 1 . So his new average is 96+1 = 97 which is greater than ayesha's . Other will clearly have a lower average than these both. Hence option E.Â
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