Let's break down and solve each part of the problem step-by-step:
### Part (1): Calculating Daks' Score
1. Total Questions:
- Daks attempts all 15 questions.
2. Percentage of Correct Answers:
- Daks correctly answers 40% of the questions.
3. Number of Correct Answers:
- 40% of 15 questions is calculated as:
[tex]\[
\text{Correct Answers} = \frac{40}{100} \times 15 = 6 \text{ answers}
\][/tex]
4. Number of Incorrect Answers:
- Since Daks attempts all the questions and answers 6 questions correctly, the number of incorrect answers is:
[tex]\[
\text{Incorrect Answers} = 15 - 6 = 9 \text{ answers}
\][/tex]
5. Scoring:
- Marks per correct answer: 4 marks.
- Marks per incorrect answer: -2 marks.
6. Calculating Daks' Total Score:
- Total score from correct answers:
[tex]\[
\text{Score from Correct Answers} = 6 \times 4 = 24 \text{ marks}
\][/tex]
- Total score from incorrect answers:
[tex]\[
\text{Score from Incorrect Answers} = 9 \times (-2) = -18 \text{ marks}
\][/tex]
- Total score:
[tex]\[
\text{Total Score for Daks} = 24 + (-18) = 6 \text{ marks}
\][/tex]
### Part (2): Calculating Satvik's Score
1. Total Questions:
- Satvik also has a total of 15 questions.
2. Number of Correct Answers:
- Satvik answers 4 questions correctly.
3. Number of Not Attempted Questions:
- Satvik does not attempt 8 questions.
4. Number of Incorrect Answers:
- Since Satvik did not attempt 8 questions and answered 4 questions correctly, the number of incorrect answers is:
[tex]\[
\text{Incorrect Answers} = 15 - 4 - 8 = 3 \text{ answers}
\][/tex]
5. Scoring:
- Marks per correct answer: 4 marks.
- Marks per incorrect answer: -2 marks.
6. Calculating Satvik's Total Score:
- Total score from correct answers:
[tex]\[
\text{Score from Correct Answers} = 4 \times 4 = 16 \text{ marks}
\][/tex]
- Total score from incorrect answers:
[tex]\[
\text{Score from Incorrect Answers} = 3 \times (-2) = -6 \text{ marks}
\][/tex]
- Total score:
[tex]\[
\text{Total Score for Satvik} = 16 + (-6) = 10 \text{ marks}
\][/tex]
### Summary
- Daks' Score:
- Correct Answers: 6
- Incorrect Answers: 9
- Total Score: 6 marks
- Satvik's Score:
- Correct Answers: 4
- Not Attempted: 8
- Incorrect Answers: 3
- Total Score: 10 marks
