In a test, 4 marks are given for every correct answer and -2 marks for every incorrect answer. Asha answered all the questions and scored 26 marks though she got nine correct answers. Varun also answered all he questions and scored 2 marks though he got five correct answers. How many questions did each of them answer incorrectly?

Options

A. 10,8
B. 9,18
C. 5,9
D. 4,10

Answer

To solve the problem, we need to determine how many questions Asha and Varun answered incorrectly based on their scores and the number of correct answers they provided.

### Step-by-Step Solution

1. **Identify the scoring system**:
- Each correct answer gives 4 marks.
- Each incorrect answer deducts 2 marks.

2. **Set up the equations for Asha**:
- Let \( x \) be the number of incorrect answers Asha gave.
- Asha got 9 correct answers, so the total number of questions she answered is \( 9 + x \).
- The score for Asha can be calculated as:
\[ \text{Score} = (4 \times \text{correct answers}) + (-2 \times \text{incorrect answers}) \]
Substituting the values:
\[ 26 = (4 \times 9) + (-2 \times x) \]
Simplifying this gives:
\[ 26 = 36 - 2x \]
Rearranging the equation:
\[ 2x = 36 - 26 \]
\[ 2x = 10 \]
\[ x = 5 \]
- Therefore, Asha answered **5 questions incorrectly**.

3. **Set up the equations for Varun**:
- Let \( y \) be the number of incorrect answers Varun gave.
- Varun got 5 correct answers, so the total number of questions he answered is \( 5 + y \).
- The score for Varun can be calculated as:
\[ 2 = (4 \times 5) + (-2 \times y) \]
Simplifying this gives:
\[ 2 = 20 - 2y \]
Rearranging the equation:
\[ 2y = 20 - 2 \]
\[ 2y = 18 \]
\[ y = 9 \]
- Therefore, Varun answered **9 questions incorrectly**.

### Final Answer:
- Asha answered 5 questions incorrectly.
- Varun answered 9 questions incorrectly.