The following question came from IIT- Class 8 (Math) - Linear equations and inequalities (Pearson publications) :
In a test, one mark is awarded for each correct answer and 0.5 marks are deducted for each incorrect answer. A student attempted all the questions in the test. If the mark(s) awarded for each correct answer and marks deducted for each incorrect answer are interchanged, he would have got 90 marks less than what he actually got. Find the number of questions in the test.
I did the sum the following way:
Let m be the number of correct answers and n be the number of incorrect answers.
So, the total number of questions = m+n
From the question:
m - (n/2) = (m/2) -n +90
(m+n)/2 = 90
(m+n) = 180
which is not in accordance with any of the options. What have I done wrong?