The problem involves two students, A and B, who have attempted a certain number of questions in an exam and received certain scores. The scoring system involves both positive marks for correct answers and negative marks for incorrect answers. The negative marking scheme is such that the first 20 incorrect answers have a different negative mark value than the remaining incorrect answers. We are asked to find the negative mark value for each incorrect answer beyond the first 20.

Let's break down the problem step by step:

1. Student A attempted 160 questions and correctly answered 50% of them. This means A answered 80 questions correctly. Since each correct answer fetches one mark, A got 80 marks from correct answers. But A's total score is 55, which means A lost 25 marks for incorrect answers.

2. Student B attempted 150 questions and correctly answered 6623% of them. This seems to be a typo because a percentage cannot be more than 100%. Assuming it's a typo and the correct percentage is 66.23%, B answered approximately 99 questions correctly (150 * 0.6623 ≈ 99). So, B got approximately 99 marks from correct answers. But B's total score is 85, which means B lost approximately 14 marks for incorrect answers.

3. Now, let's consider the negative marking scheme. For the first 20 incorrect answers, the negative mark value is unknown but it's the same for both A and B. For the remaining incorrect answers, the negative mark value is also unknown and it's what we are asked to find.

4. Student A answered 80 questions incorrectly (160 total attempts - 80 correct answers = 80 incorrect answers). The first 20 of these incorrect answers have a different negative mark value than the remaining 60 incorrect answers.

5. Student B answered approximately 51 questions incorrectly (150 total attempts - 99 correct answers ≈ 51 incorrect answers). All of these incorrect answers have the same negative mark value because the number of incorrect answers is less than or equal to 20.

6. Since A lost 25 marks for 80 incorrect answers and B lost approximately 14 marks for 51 incorrect answers, we can set up the following equation to solve for the unknowns:

20x + 60y = 25 (equation 1 for A)

51x = 14 (equation 2 for B)

Here, x is the negative mark value for the first 20 incorrect answers and y is the negative mark value for each incorrect answer beyond the first 20.

7. Solving equation 2 for x gives x = 14/51 ≈ 0.27.

8. Substituting x = 0.27 into equation 1 gives 20*0.27 + 60y = 25, which simplifies to 5.4 + 60y = 25. Solving this for y gives y = (25 - 5.4) / 60 ≈ 0.33.

So, the negative mark for each wrong answer beyond the first twenty wrong answers is approximately 0.33.

Question

The problem involves two students, A and B, who have attempted a certain number of questions in an exam and received certain scores. The scoring system involves both positive marks for correct answers and negative marks for incorrect answers. The negative marking scheme is such that the first 20 incorrect answers have a different negative mark value than the remaining incorrect answers. We are asked to find the negative mark value for each incorrect answer beyond the first 20.

Let's break down the problem step by step:

1. Student A attempted 160 questions and correctly answered 50% of them. This means A answered 80 questions correctly. Since each correct answer fetches one mark, A got 80 marks from correct answers. But A's total score is 55, which means A lost 25 marks for incorrect answers.

2. Student B attempted 150 questions and correctly answered 6623% of them. This seems to be a typo because a percentage cannot be more than 100%. Assuming it's a typo and the correct percentage is 66.23%, B answered approximately 99 questions correctly (150 * 0.6623 ≈ 99). So, B got approximately 99 marks from correct answers. But B's total score is 85, which means B lost approximately 14 marks for incorrect answers.

3. Now, let's consider the negative marking scheme. For the first 20 incorrect answers, the negative mark value is unknown but it's the same for both A and B. For the remaining incorrect answers, the negative mark value is also unknown and it's what we are asked to find.

4. Student A answered 80 questions incorrectly (160 total attempts - 80 correct answers = 80 incorrect answers). The first 20 of these incorrect answers have a different negative mark value than the remaining 60 incorrect answers.

5. Student B answered approximately 51 questions incorrectly (150 total attempts - 99 correct answers ≈ 51 incorrect answers). All of these incorrect answers have the same negative mark value because the number of incorrect answers is less than or equal to 20.

6. Since A lost 25 marks for 80 incorrect answers and B lost approximately 14 marks for 51 incorrect answers, we can set up the following equation to solve for the unknowns:

20x + 60y = 25 (equation 1 for A)
    
    51x = 14 (equation 2 for B)

Here, x is the negative mark value for the first 20 incorrect answers and y is the negative mark value for each incorrect answer beyond the first 20.

7. Solving equation 2 for x gives x = 14/51 ≈ 0.27.

8. Substituting x = 0.27 into equation 1 gives 20*0.27 + 60y = 25, which simplifies to 5.4 + 60y = 25. Solving this for y gives y = (25 - 5.4) / 60 ≈ 0.33.

So, the negative mark for each wrong answer beyond the first twenty wrong answers is approximately 0.33.

Knowee AI · Accepted Answer