The rules of the examination are…
● A correct answer gets +3 marks.
● A wrong answer gets -1 mark.
● An unanswered question gets +1 mark.
So, the scenario is, every question is already awarded 1 mark before attempting, if the attempt is right you get +2 marks and if it is wrong you get -2 marks.
So after re-imagining the examination…
● Every Question is awarded + 1 before attempting itself.
(This means you enter the examination with 75 marks in your pocket)
● A right answer fetches +2 marks.
● A wrong answer fetches -2 marks.
Now it is up to the student to increase or decrease his total marks from 75.
If he answers more questions right than wrong he gets additional marks.
If he answers more questions wrong than right his marks decrease.
So, when Rayan scored a total of 97 marks in the examination, 75 were given to him on a platter. The remaining 22 is what he put effort to score.
This means the difference between the number of questions he got right and the number of questions he got wrong is 11.
In the most extreme case, he might have got 11 questions right and did not attempt the remaining.

He might have got a few questions wrong, but the number of right questions should always be more than the number of wrong questions by 11.
The case where the number of wrong questions is ‘x’ looks like…

The number of unattempted questions was higher than the number of attempted questions…
This means,
 64 - 2x > 11 + x + x
53 > 4x
x≤13x≤13.
The maximum value of x is 13.
The maximum number of the right answers = 11 + 13 = 24