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