X attempts 100 questions and gets 340 marks. If for every correct answer is 4 marks and wrong answer is negative one mark, then the number of questions wrongly answered by Mr. X is :

Options

A. 14
B. 15
C. 12
D. 13

Answer

To solve the problem, we need to set up equations based on the information given.

1. **Define Variables:**
Let:
- \( C \) = Number of correct answers
- \( W \) = Number of wrong answers

2. **Set Up Equations:**
From the problem, we know:
- The total number of questions attempted is 100.
- The total marks scored is 340.
- Each correct answer gives 4 marks, and each wrong answer deducts 1 mark.

We can write the following equations:
\[ C + W = 100 \quad \text{(1)} \]
\[ 4C - W = 340 \quad \text{(2)} \]

3. **Solve the Equations:**
From equation (1), we can express \( W \) in terms of \( C \):
\[ W = 100 - C \quad \text{(3)} \]

Now, substitute equation (3) into equation (2):
\[ 4C - (100 - C) = 340 \]
Simplifying this gives:
\[ 4C - 100 + C = 340 \]
\[ 5C - 100 = 340 \]
\[ 5C = 440 \]
\[ C = \frac{440}{5} = 88 \]

4. **Find the Number of Wrong Answers:**
Now, substitute \( C \) back into equation (3) to find \( W \):
\[ W = 100 - 88 = 12 \]

5. **Conclusion:**
Therefore, the number of questions wrongly answered by Mr. X is \( 12 \).