Q10. In a test, (+5) marks are given for every correct answer and (-2) marks are given for every incorrect answer.

(i) Rohan answered all the questions and scored 24 marks even though he got 8 correct answers. How many incorrect answers did he attempt?



Answer :

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.