To find the number of questions Aman answered incorrectly, let's proceed step-by-step:
1. Identify Given Values:
- Total marks scored by Aman: [tex]\( 29 \)[/tex]
- Number of correct answers: [tex]\( 7 \)[/tex]
- Marks per correct answer: [tex]\( +5 \)[/tex]
- Marks per incorrect answer: [tex]\( -2 \)[/tex]
2. Calculate the Marks from Correct Answers:
Since Aman got 7 correct answers and each correct answer gives him 5 marks, we can calculate the total marks from correct answers:
[tex]\[
\text{Marks from correct answers} = 7 \times 5 = 35
\][/tex]
3. Determine Marks Contributed by Incorrect Answers:
We know the total marks (29) and the marks from correct answers (35). The difference between these two will give us the marks contributed by incorrect answers:
[tex]\[
\text{Marks from incorrect answers} = 29 - 35 = -6
\][/tex]
Since incorrect answers contribute -2 marks each, these -6 marks result from some incorrect answers.
4. Calculate the Number of Incorrect Answers:
To find the number of incorrect answers, we divide the total negative marks by the marks deducted per incorrect answer:
[tex]\[
\text{Number of incorrect answers} = \frac{\text{Marks from incorrect answers}}{\text{Marks per incorrect answer}} = \frac{-6}{-2} = 3
\][/tex]
Therefore, Aman attempted incorrectly 3 questions.
