There are 180 multiple choice questions in a test. A candidate gets 4 marks for every correct answer, and for every un-attempted or wrongly answered questions one mark is deducted from the total score of correct answers. If a candidate scored 450 marks in the test how many questions did he answer correctly?

Number of multiple choice questions = 180

Let the number of correct answers be x.

∴ The number of wrongly answered questions = 180 – x.

The marks awarded for every correct answer = 4.

∴ The score of correct answers = 4x.

The marks deducted for every wrong answer = 1.

∴ The total marks deducted = 1 (180 – x) = 180 – x.

The total score of the candidate = 450.

According to the given condition,

4x – (180 – x) = 450

⇒ 4x – 180 + x = 450 (Removing bracket)

5x – 180 = 450

⇒ 5x = 450 + 180 (Transposing 180 to RHS)

5x = 630

⇒ x = (Transposing 5 to RHS)

x = 126

∴ The number of questions that the candidate answered correctly is 126.