In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. A student attempted all the 200 questions and scored in all 200 marks. The number of questions, he answered correctly was

Options

A. 82
B. 80
C. 68
D. 60

Answer

To solve the problem, we need to determine how many questions the student answered correctly based on the scoring system provided.

### Step-by-Step Solution:

1. **Define Variables**:
Let \( x \) be the number of correct answers the student gave.

2. **Determine Incorrect Answers**:
Since the student attempted all 200 questions, the number of incorrect answers will be \( 200 - x \).

3. **Calculate Total Marks**:
The student scores 4 marks for each correct answer and loses 1 mark for each incorrect answer. Therefore, the total score can be expressed as:
\[ \text{Total Score} = (4 \times \text{Number of Correct Answers}) - (1 \times \text{Number of Incorrect Answers}) \]
Substituting the variables we defined:
\[ \text{Total Score} = 4x - (200 - x) \]

4. **Set Up the Equation**:
According to the problem, the total score is 200 marks. Thus, we can set up the equation:
\[ 4x - (200 - x) = 200 \]

5. **Simplify the Equation**:
Simplifying the left-hand side:
\[ 4x - 200 + x = 200 \]
Combine like terms:
\[ 5x - 200 = 200 \]

6. **Solve for \( x \)**:
Add 200 to both sides:
\[ 5x = 400 \]
Now, divide both sides by 5:
\[ x = 80 \]

7. **Conclusion**:
Therefore, the number of questions the student answered correctly is \( \boxed{80} \).