In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :

Options

A. A) 35
B. B) 38
C. C) 40
D. D) 42

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define Variables
Let \( x \) be the number of questions answered correctly by the student.

### Step 2: Determine Incorrect Answers
Since the student attempts a total of 60 questions, the number of questions answered incorrectly would be:
\[ 60 - x \]

### Step 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:
\[ \text{Total Marks} = 4x - (60 - x) \]
This simplifies to:
\[ \text{Total Marks} = 4x - 60 + x = 5x - 60 \]

### Step 4: Set Up the Equation
According to the problem, the total marks obtained by the student is 130. Therefore, we can set up the equation:
\[ 5x - 60 = 130 \]

### Step 5: Solve for \( x \)
Now, we will solve the equation for \( x \):
\[ 5x - 60 = 130 \]
Add 60 to both sides:
\[ 5x = 130 + 60 \]
\[ 5x = 190 \]
Now, divide both sides by 5:
\[ x = \frac{190}{5} = 38 \]

### Conclusion
The number of questions the student attempted correctly is:
\[ \boxed{38} \]

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