In an examination, a student got 150 marks if he answered all the 75 question. He got 4 marks for each right answer and 2 marks are deducted for watch wrong answer from his score. Total right answer are

Options

A. 45
B. 50
C. 55
D. 48

Answer

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

### Step 1: Define Variables
Let:
- \( x \) = number of correct answers
- \( y \) = number of wrong answers

From the problem, we know:
- Total questions answered = 75
- Total marks obtained = 150
- Marks for each correct answer = 4
- Marks deducted for each wrong answer = 2

### Step 2: Set Up Equations
We can set up the following equations based on the information provided:

1. The total number of questions answered:
\[ x + y = 75 \]

2. The total marks obtained:
\[ 4x - 2y = 150 \]

### Step 3: Solve the First Equation for \( y \)
From the first equation, we can express \( y \) in terms of \( x \):
\[ y = 75 - x \]

### Step 4: Substitute \( y \) in the Second Equation
Now, substitute \( y \) in the second equation:
\[ 4x - 2(75 - x) = 150 \]

### Step 5: Simplify the Equation
Distributing the -2:
\[ 4x - 150 + 2x = 150 \]
Combine like terms:
\[ 6x - 150 = 150 \]

### Step 6: Solve for \( x \)
Add 150 to both sides:
\[ 6x = 300 \]
Divide by 6:
\[ x = 50 \]

### Step 7: Find \( y \)
Now, substitute \( x \) back into the equation for \( y \):
\[ y = 75 - 50 = 25 \]

### Conclusion
The student answered **50 questions correctly**.