Scoring with positive and negative marks Mohan gets +3 for each correct answer and −2 for each wrong answer. He attempts 30 questions and scores 40 marks in total. How many answers did he get correct?

Introduction / Context:This is a linear system framed by total attempts and net score under positive and negative marking. We create two equations and solve for the number of correct answers.

Given Data / Assumptions:

• Total attempts = 30.
• Marks: +3 per correct, −2 per wrong.
• Total score = 40.

Concept / Approach:Let c be the number of correct answers and w be the number of wrong answers. Then c + w = 30 and 3c − 2w = 40. Solve the system by substitution or elimination.

Step-by-Step Solution:From c + w = 30, we get w = 30 − c.Substitute into 3c − 2w = 40 → 3c − 2(30 − c) = 40.Simplify: 3c − 60 + 2c = 40 → 5c = 100.Hence c = 100/5 = 20.

Verification / Alternative check:Compute score with c = 20, w = 10: 20 × 3 − 10 × 2 = 60 − 20 = 40, which matches.

Why Other Options Are Wrong:25, 10, 15, and 18 do not satisfy both equations simultaneously.

Common Pitfalls:Mixing up signs for wrong answers or forgetting that c + w must equal 30.

Final Answer:20