In a management entrance test, a student scores 2 marks for every correct answer and loses 0.5 marks for every wrong answer. A student attempts all the 100 questions and scores 120 marks. The number of questions he answered correctly was
(a)50
(b)45
(c)60
(d)68

Options

A. 50
B. 45
C. 60
D. 68

Answer

To solve the problem, we can set up a system of equations based on the information given:

1. Let \( x \) be the number of correct answers.
2. Let \( y \) be the number of wrong answers.

From the problem, we know:
- The total number of questions attempted is 100:
\[ x + y = 100 \]

- The scoring system awards 2 marks for each correct answer and deducts 0.5 marks for each wrong answer. The total score is 120:
\[ 2x - 0.5y = 120 \]

Now we have a system of two equations:
1. \( x + y = 100 \) (Equation 1)
2. \( 2x - 0.5y = 120 \) (Equation 2)

### Step 1: Solve Equation 1 for \( y \)
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 100 - x \]

### Step 2: Substitute \( y \) in Equation 2
Now, we substitute \( y \) in Equation 2:
\[ 2x - 0.5(100 - x) = 120 \]

### Step 3: Simplify the equation
Distributing the -0.5:
\[ 2x - 50 + 0.5x = 120 \]
Combine like terms:
\[ 2.5x - 50 = 120 \]

### Step 4: Solve for \( x \)
Add 50 to both sides:
\[ 2.5x = 170 \]
Now, divide by 2.5:
\[ x = \frac{170}{2.5} = 68 \]

### Step 5: Find \( y \)
Now, substitute \( x = 68 \) back into Equation 1 to find \( y \):
\[ y = 100 - 68 = 32 \]

### Conclusion
The number of questions answered correctly is \( x = 68 \).

Thus, the answer is (d) 68.

---