Question
In a test paper, correct answers fetch three marks and there is a penalty of one mark for each wrong answer. A student who attempts 76 questions gets 144 marks. How many questions did the student get right?
This question was previously asked in
RRB NTPC 2019 CBT 1 Question Paper PDF (31-Jan-2021) (Shift 1)
The correct answer is
55
Solving the Test Paper Marks Problem
This problem involves calculating the number of correct answers based on the total questions attempted, the marks awarded for correct answers, the penalty for wrong answers, and the final score.
Set Up the Variables
- Let $ c $ represent the number of questions answered correctly.
- Let $ w $ represent the number of questions answered incorrectly.
Formulate Equations
From the question, we have two key pieces of information:
- The total number of questions attempted is 76: $ c + w = 76 $
- The total marks obtained is 144, with +3 for correct and -1 for wrong: $ 3c - w = 144 $
Alternative Solution Method (Exam Focused)
- Assume all attempts were correct: If all 76 questions were answered correctly, the total marks would be $ 76 \times 3 = 228 $ marks.
- Calculate the difference in marks: The student scored 144 marks, which is $ 228 - 144 = 84 $ marks less than the maximum possible score assuming all were correct.
- Determine the mark difference per wrong answer: Each wrong answer costs 1 mark (penalty) and loses the 3 marks that would have been awarded if correct. So, each wrong answer results in a total difference of $ 3 + 1 = 4 $ marks compared to a correct answer.
- Calculate the number of wrong answers: Divide the total mark difference by the difference per wrong answer: $ \frac{84}{4} = 21 $ wrong answers.
- Calculate the number of correct answers: Subtract the number of wrong answers from the total questions attempted: $ 76 - 21 = 55 $ correct answers.
Verification
Check the result: $ 55 $ correct answers and $ 21 $ wrong answers.
- Total Questions: $ 55 + 21 = 76 $ (Correct)
- Total Marks: $ (55 \times 3) - (21 \times 1) = 165 - 21 = 144 $ (Correct)
Therefore, the student answered 55 questions correctly.
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