To determine how many incorrect answers Rohan had attempted, we'll go through a step-by-step solution using the information provided:
1. Identify the marks for correct and incorrect answers:
- Marks for a correct answer: [tex]\( +5 \)[/tex]
- Marks for an incorrect answer: [tex]\( -2 \)[/tex]
2. Understand Rohan's performance:
- Rohan's total score: [tex]\( 24 \)[/tex] marks
- Number of correct answers: [tex]\( 8 \)[/tex]
3. Calculate the total score from Rohan's correct answers:
- Number of correct answers: [tex]\( 8 \)[/tex]
- Each correct answer gives [tex]\( +5 \)[/tex] marks
- Total score from correct answers: [tex]\( 8 \times 5 = 40 \)[/tex] marks
4. Calculate the total score Rohan lost due to incorrect answers:
- Total score: [tex]\( 24 \)[/tex] marks
- Total score from correct answers: [tex]\( 40 \)[/tex] marks
- So, the total marks due to incorrect answers must be:
[tex]\[
\text{Total score} - \text{Score from correct answers} = 24 - 40 = -16
\][/tex]
5. Determine the number of incorrect answers:
- Each incorrect answer deducts [tex]\( 2 \)[/tex] marks ([tex]\( -2 \)[/tex] marks)
- Total score lost due to incorrect answers: [tex]\( -16 \)[/tex] marks
- Number of incorrect answers: [tex]\(\frac{-16}{-2} = 8 \)[/tex]
So, Rohan had attempted 8 incorrect answers.
