Question

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.

Answer 1

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.

Answer 2

Got it.thanks