Question

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

• A. $20$
• B. $40$
• C. $50$
• D. $100$

Answer 1

The correct option is C $50$

$\Rightarrow$ 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 $n$

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

$\Rightarrow$ $15+\frac{1}{3}(n-20)=\frac{n}{2}$

$\Rightarrow$ $90+2(n-20)=3n$

$\Rightarrow$ $90+2n-40=3n$

$\therefore$ $n=50$