The maximum possible score in an exam was 80 and all questions carried equal weightage. For each correct answer 4 marks were awarded whereas for each wrong answer 1 mark was deducted. For no answer, the marks remained unchanged. A student got 57 marks in which he failed to attempt only 2 questions. Answer the number of questions he got correct as a percentage of total number of questions.
I think you want to ask how are such questions solved
If x answers were correct and y were wrong
then x-o.5y= 54.5 --- (1)
and
assuming he/she attempted all questions
x+y = 80 ----(2)
solving 1 and 2
1.5y = 25.5 => y = 17
If the number of questions attempted are variable, then you have to put a constraint that x+y can only be an integer
The second constraint is 1.5y should have .5 as the least significant figure (after decimal)
The third constraint is y can never be more than 17
suppose y is 16, then 1.5 y is 24, which breaks the second constraint
suppose y is 15, then 1.5 y is 22.5, which is a valid answer if he/she attempted 77 questions, x is 62 in this case.
Got it.thanks
To find out the number of questions the student got correct as a percentage of the total number of questions, we first need to determine the number of questions attempted.
We know that the student received 57 marks, but failed to attempt only 2 questions. So, we can calculate the number of questions attempted using the following equation:
Number of questions attempted = 80 - Number of questions not attempted
Since the student failed to attempt 2 questions:
Number of questions attempted = 80 - 2
= 78
Now, let's calculate the total number of correct answers. We know that each correct answer is awarded 4 marks, so:
Total marks for correct answers = Number of correct answers * 4
Since we don't know the number of correct answers, let's assume it as 'x':
Total marks for correct answers = x * 4
According to the given information, the student received 57 marks:
Total marks for correct answers - Number of incorrect answers = 57
(x * 4) - (Number of incorrect answers * 1) = 57
But we don't know the number of incorrect answers either. However, we can find it by subtracting the number of correct answers from the total number of questions attempted:
Number of incorrect answers = Number of questions attempted - Number of correct answers
Substituting this value in the previous equation:
(x * 4) - ((Number of questions attempted - Number of correct answers) * 1) = 57
Now, we can simplify the equation:
4x - (78 - x) = 57
Solving for 'x':
4x - 78 + x = 57
5x - 78 = 57
5x = 57 + 78
5x = 135
x = 135/5
x = 27
Therefore, the student got 27 questions correct.
To find the percentage, we divide the number of correct answers by the total number of questions attempted:
Percentage of correct answers = (Number of correct answers / Total number of questions attempted) * 100
Percentage of correct answers = (27 / 78) * 100
Percentage of correct answers ≈ 34.62%
So, the number of questions the student got correct is approximately 34.62% of the total number of questions.