Question

In an examination, a candidate scores 2 marks for every correct answer and loses 1 mark for every wrong answer. A candidate attempts all the 100 questions and scores 56 marks. How many questions did he answer correctly?

• A. 52
• B. 48
• C. 60
• D. 56

Hint:

Using the elimination method (adding/subtracting equations) is usually faster for these types of problems.

Answer 1

The Correct Option is A

Step 1: Set up the unknowns.
Let the number of correct answers be $x$ and wrong answers be $y$.

Step 2: Total questions.
He attempts all 100 questions, so $x + y = 100$.

Step 3: Total marks.
Each correct gives 2 marks and each wrong takes away 1 mark, and the total is 56. So $2x - y = 56$.

Step 4: Add the two equations.
Adding them removes $y$. We get \[ (x + y) + (2x - y) = 100 + 56 \] which gives $3x = 156$.

Step 5: Solve for x.
So $x = \frac{156}{3} = 52$.

Step 6: Conclusion.
He answered 52 questions correctly.
Answer: 52