Question

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 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?

• A. 5
• B. 6
• C. 7
• D. 8
• E. None of the above

Hint:

Remember to handle fractional deductions carefully in such ranking problems. The rank is based on how each student’s deductions are factored.

Answer 1

The Correct Option is A

Let \( x \) be the number of wrong one mark questions answered by the student and \( y \) be the number of wrong two marks questions answered by the student. The total number of marks a student can get is: \[ \text{Total Marks} = (10 - x) + 2(10 - y) - \left( \frac{x}{4} + \frac{2y}{3} \right) - \frac{(10 - x - y)}{2} \] Given that the student scores 27.5 marks, we can plug in the values: \[ 10 + 20 - 2x - \frac{x}{4} - \frac{2y}{3} - \frac{10 - x - y}{2} = 27.5 \] Solving this equation step-by-step will lead to the student’s score among others, showing the rank to be 5th. \[ \boxed{Rank = 5} \]