In a competitive test, Hemavathi scores +3 marks for each correct answer and loses 2 marks for each wrong answer. She attempts a total of 35 questions and her final score is 60 marks. How many questions does she answer correctly?

Introduction:
This question tests forming and solving a simple linear system from a marks scheme. Many aptitude tests award positive marks for correct answers and deduct marks for wrong ones (negative marking). The key idea is that the total attempts split into correct and wrong, and the total score is a weighted sum using the given marks per correct and per wrong. Once you translate the words into two equations, the answer follows with basic algebra.

Given Data / Assumptions:

• Marks per correct answer = +3
• Marks per wrong answer = -2
• Total questions attempted = 35
• Total score obtained = 60
• Let correct answers = c, wrong answers = w

Concept / Approach:
Use two facts: (1) c + w equals total attempts, and (2) 3c - 2w equals total score. Solve the pair of linear equations. A standard shortcut is to substitute w = 35 - c into the score equation to get a single equation in c.

Step-by-Step Solution:
c + w = 35 3c - 2w = 60 Substitute w = 35 - c into the score equation 3c - 2(35 - c) = 60 3c - 70 + 2c = 60 5c = 130 c = 26

Verification / Alternative check:
If c = 26, then w = 35 - 26 = 9. Score = 3*26 - 2*9 = 78 - 18 = 60, which matches the given total score exactly.

Why Other Options Are Wrong:
24 gives w = 11 and score 72 - 22 = 50. 25 gives score 75 - 20 = 55. 23 gives score 69 - 24 = 45. 27 gives score 81 - 16 = 65. Only 26 produces 60.

Common Pitfalls:
Forgetting negative marking (treating wrong as +2), using total questions instead of attempted questions, or mixing up c and w during substitution.

Final Answer:
Hemavathi answers 26 questions correctly.