Question

In an examination, a candidate attempts $90\%$ of the total questions. Out of these, $70\%$ of his answers are correct. Each question carries $3$ marks for the correct answer and $(-1)$ mark for the wrong answer. If the marks secured by the candidate is $243$, what is the total number of questions?

• A. $110$
• B. $140$
• C. $150$
• D. $200$

Answer 1

Answer: (C)

$150$

Let the total number of questions be $x$.

Number of questions attempted $=90\%\times x=0.9x$

Number of correct answers $=70\%\times 0.9x=0.7\times 0.9x=0.63x$

Number of incorrect answers $=30\%\times 0.9x=0.3\times 0.9x=0.27x$

According to the question, we have

$0.63x\times 3+0.27x\times (-1)=243$

$\Rightarrow 1.89x-0.27x=243$

$\Rightarrow 1.62x=243$

$\Rightarrow x=\frac{243}{1.62}=\frac{24300}{162}=150$