In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. The student attempts all 60 questions and secures a total of 130 marks. How many questions did the student answer correctly?

Introduction / Context:
This problem checks algebraic reasoning in the context of an exam marking scheme. Marks are awarded for correct answers and deducted for wrong ones. The total marks and total number of attempts are known, and we must find how many questions were answered correctly. Such questions appear frequently in quantitative aptitude tests, especially for bank and management entrance exams.

Given Data / Assumptions:

• Total questions attempted = 60.
• Marks for each correct answer = +4.
• Marks for each wrong answer = −1.
• Total marks obtained by the student = 130.
• Let the number of correct answers be x.
• Since all 60 are attempted, the number of wrong answers is 60 − x.

Concept / Approach:
The idea is to translate the marking scheme into an equation. Total marks come from correct answers giving positive marks and wrong answers giving negative marks. We set up a linear equation in terms of the number of correct answers x and solve it. This is a standard linear word problem.

Step-by-Step Solution:
Let the number of correct answers be x.Then the number of wrong answers is 60 − x.Total marks = 4 × (number of correct answers) − 1 × (number of wrong answers).So, 4x − (60 − x) = 130.Simplify: 4x − 60 + x = 130, which becomes 5x − 60 = 130.Add 60 to both sides: 5x = 190.Divide by 5: x = 190 / 5 = 38.

Verification / Alternative check:
If the student answered 38 questions correctly, then wrong answers = 60 − 38 = 22. Marks from correct answers = 38 × 4 = 152. Negative marks from wrong answers = 22 × 1 = 22. Net score = 152 − 22 = 130, which matches the given total. Any other value of x would produce a different total mark and would not equal 130.

Why Other Options Are Wrong:
If x = 35, then wrong answers = 25 and the total score is 35 × 4 − 25 = 115. If x = 40, wrong answers = 20 and the score is 160 − 20 = 140. For x = 42, score becomes 168 − 18 = 150. For x = 32, the score is 128 − 28 = 100. None of these totals equals 130, so those options are incorrect.

Common Pitfalls:
Students sometimes forget that all 60 questions are attempted and may assume some were left blank. Others mistakenly add the wrong answer penalty instead of subtracting it. A sign error in forming the equation, such as writing 4x + (60 − x), changes the result completely. Carefully setting up the equation with correct signs is essential for success.

Final Answer:
The student answered 38 questions correctly.