Question

In an examination of $n$ question, a student replied $15$ out of the first $20$ questions correctly. Of the remaining questions, he answered one-third correctly. All the question having same credit. If the student gets $50$% marks, the value of $n$ is.

• A. $20$
• B. $90$
• C. $50$
• D. $100$

Answer 1

The correct option is C $50$

Student attempts $n$ questions.

$\Rightarrow$ Out of $20$ question he answers $15$ correctly and of $(n-20)$ questions he answered $\frac{1}{3}$ correctly.

$\Rightarrow$ The student gets $50\%$ marks.

$\therefore 15+\frac{1}{3}(n-20)=50\%$ of $n$

$\Rightarrow 15+\frac{1}{3}(n-20)=\frac{50}{100}n$

$\Rightarrow 15+\frac{n}{3}-\frac{20}{3}=\frac{n}{2}$

$\Rightarrow \frac{45-20}{3}=\frac{n}{2}-\frac{n}{3}$

$\Rightarrow \frac{25}{3}=\frac{3n-2n}{6}$

$\Rightarrow 25=\frac{n}{2}$

$\therefore n=50$