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 80 marks. How many questions did he answer correctly?
A. 80 B. 60 C. 20 D. 100
Correct Answer: B
Explanation
To find out how many questions the candidate answered correctly, follow these steps:
1. Define Variables: - Let \( x \) be the number of correct answers. - Let \( y \) be the number of wrong answers.
2. Set Up Equations: - The total number of questions is 100, so: \[ x + y = 100 \]
- The scoring system gives 2 marks for each correct answer and loses 1 mark for each wrong answer. The candidate scores 80 marks, so: \[ 2x - y = 80 \]
3. Solve the System of Equations:
Substitute \( y \) from the first equation into the second equation: \[ y = 100 - x \] \[ 2x - (100 - x) = 80 \] Simplify and solve for \( x \): \[ 2x - 100 + x = 80 \] \[ 3x - 100 = 80 \] \[ 3x = 180 \] \[ x = 60 \]
