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?
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Correct Answer: Option 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 \( x \):
\[
2x - 100 + x = 80
\]
\[
3x - 100 = 80
\]
\[
3x = 180
\]
\[
x = 60
\]
So, the number of correct answers is 60.
The candidate answered 60 questions correctly.
The correct answer is B. 60.
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 \( x \):
\[
2x - 100 + x = 80
\]
\[
3x - 100 = 80
\]
\[
3x = 180
\]
\[
x = 60
\]
So, the number of correct answers is 60.
The candidate answered 60 questions correctly.
The correct answer is B. 60.