Question

There are 180 multiple choice questions in a test. If a candidate gets 4 marks for every correct answer and for every unattempted or wrongly answered question 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?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{correctly}\mathrm{answered}\mathrm{questions}\mathrm{be}x. \\ \mathrm{Therefore},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{unattempted}\mathrm{or}\mathrm{wrongly}\mathrm{answered}\mathrm{questions}\mathrm{will}\mathrm{be}(180-\mathrm{x}). \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}, \\ 4\mathrm{x}-1(180-\mathrm{x})=450 \\ \mathrm{or}5\mathrm{x}=450+180 \\ \mathrm{or}\mathrm{x}=\frac{630}{5}=126 \\ \mathrm{Thus},\mathrm{number}\mathrm{of}\mathrm{correctly}\mathrm{answered}\mathrm{questions}=126. \\ \mathrm{Number}\mathrm{of}\mathrm{unattempted}\mathrm{or}\mathrm{wrongly}\mathrm{answered}\mathrm{questions}=180-126=54. \end{gathered}$$