Answered

1. In a class test of 15 questions, 4 marks are given for every correct answer, -2 marks for every incorrect answer, and no marks for unanswered questions.

(1) Daksh attempts all questions but only half of his answers are correct. What is his score?

(2) Satvik gets only 4 answers correct and does not attempt 8 questions at all. What is his score?



Answer :

GinnyAnswer
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

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