In a multiple-choice examination, there are 20 questions. Each correct answer is worth 4 marks, while 2 marks are to be deducted for every unattempted question. One student receives a total of 46 marks in the examination. However, before releasing the marks, the professor realizes that she has, by mistake, deducted 2 marks for every unattempted question and 1 mark for every wrong answer.
After correction, how many marks will the student get?
After correction, how many marks will the student get?
Show Hint
- 42
- 49
- 44
- 48
- 46
The Correct Option is
Solution and Explanation
We know the student received 46 marks, but the professor had mistakenly deducted 2 marks for unattempted questions and 1 mark for wrong answers. We need to correct this mistake.
Step 2: Let the number of correct, wrong, and unattempted questions be \( c \), \( w \), and \( u \) respectively.
Each correct answer gives 4 marks, and each wrong answer deducts 1 mark. Unattempted questions are wrongly deducted 2 marks instead of 0. Thus, the equation becomes: \[ 4c - w - 2u = 46 \] We also know: \[ c + w + u = 20 \]
Step 3: Correct the deductions.
The correction involves changing the deduction for unattempted questions from 2 marks to 0 and the deduction for wrong answers from 1 mark to 0. Therefore, the correct formula for the total marks is: \[ 4c - w = 46 \]
Step 4: Solve the equations.
Solving for \( w \) and \( c \) gives the total marks, which will remain 46 after the correction.
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