In a test, 1 mark is awarded for each correct answer and one mark is deducted for each wrong answer. If a boy answer all 20 items of the test and gets 8 marks, the number of questions answered correct by him was

Options

A. 16
B. 14
C. 12
D. 8

Answer

Let's denote the number of questions answered correctly by the boy as \( x \). Since there are a total of 20 questions, the number of questions answered incorrectly would then be \( 20 - x \).

According to the problem:
- For each correct answer, the boy earns 1 mark.
- For each wrong answer, the boy loses 1 mark.

The total score can be expressed as:
\[ \text{Total Score} = (\text{Marks for correct answers}) - (\text{Marks deducted for wrong answers}) \]
Substituting the values we have:
\[ 8 = x - (20 - x) \]

Now, let's simplify the equation:
1. Distributing the negative sign:
\[ 8 = x - 20 + x \]
2. Combining like terms:
\[ 8 = 2x - 20 \]
3. Adding 20 to both sides:
\[ 8 + 20 = 2x \]
\[ 28 = 2x \]
4. Dividing both sides by 2:
\[ x = 14 \]

Thus, the number of questions answered correctly by the boy is \( \boxed{14} \).