There are 160 multiple choice questions in a test. 4 marks are allotted for a correct answer and 1 mark is deducted for a wrong answer or un-attempted question from the total score of correct answers. If a candidate scored 400 marks in the test, how many questions did he answer correctly?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 112.
Let's denote:
The number of questions the candidate answered correctly as x.
The number of questions the candidate answered incorrectly or didn't attempt as y.
We can set up the following equations based on the given information:
x + y = 160 (Total number of questions)
4x - y = 400 (Total score, considering marks gained and deducted)
Solving these equations simultaneously:
From equation 1, we get y = 160 - x.
Substituting y in equation 2: 4x - (160 - x) = 400 5x - 160 = 400 5x = 560 x = 112
Therefore, the candidate answered 112 questions correctly.