An exam contains 60 questions. For each correct answer, a student earns +3 marks; for each wrong answer, 1 mark is deducted. A student attempts all 60 questions and secures a total of 120 marks. How many questions did the student answer correctly?

Introduction / Context:This problem tests linear equation setup in a negative marking scheme. Each response contributes either a positive score (correct) or a penalty (wrong). Because all questions were attempted, the total number of correct and wrong answers must add up to the total questions.

Given Data / Assumptions:

• Total questions = 60.
• Marking: +3 for correct; −1 for wrong.
• All questions attempted ⇒ correct + wrong = 60.
• Total score obtained = 120.

Concept / Approach:Let c be the number of correct answers. Then wrong answers are (60 − c). The total score is computed as score = 3*c − 1*(60 − c). Solve the resulting linear equation for c to find the number of correct answers.

Step-by-Step Solution:

Verification / Alternative check:With c = 45, wrong = 15. Score = 45*3 − 15*1 = 135 − 15 = 120, which matches the given total, confirming correctness.

Why Other Options Are Wrong:

• 42, 18, 15, 48: Substituting any of these into 3*c − (60 − c) does not yield 120. They fail the score equation.

Common Pitfalls:

• Writing the score as 3c − (60) instead of 3c − (60 − c).
• Forgetting that all questions were attempted, so wrong = 60 − c.

Final Answer:45