In an examination, two types of questions are asked: one mark questions and two marks questions. For each wrong answer, of one mark question, the deduction is 1/4 of a mark and for each wrong answer, of two marks question, the deduction is 1/3 of a mark. Moreover, 1/2 of a mark is deducted for any unanswered question. The question paper has 10 one mark questions and 10 two marks questions. In the examination, students got all possible marks between 25 and 30 and every student had different marks. What would be the rank of a student, who scores a total of 27.5 marks?

Option 5 : None of the above

Given:

10 question = 10 marks

10 question = 20 marks

Maximum marks in an examination = 30 marks

(1/4) marks deducted answering 1 marks question wrong

(1/2) marks deducted to not answer the question.

(1/3) marks deducted answering 2 arks question wrong

Formula Used:

As 1 wrong of 2 marks would result in 2.33 deduction (As negative in 2 marks question is 1/3 of a mark for every wrong answer)

1 wrong of 1 mark lead to deduction of 1.25

1 unattempt of 1 mark lead to deduction of 1.5

1 unattempt of 2 mark lead to deduction of 2.5 marks

Calculation:

Rank 1 = 30 All questions correct

Rank 2 = 28.75 when 1 wrong question of 1 mark

Rank 3 = 28.5 when 1 left unattempt of 1 mark

Rank 4 = 27.67 when 1 wrong question of 2 marks

Rank 5 = 27.5 when 1 left unattempt of 2 marks

Rank 6 = 27.5 when 2 wrong question of 1 mark

Rank 7 = 27.25 when 1 wrong of 1 mark and 1 unattempt of 1 mark