Question

On an examination of $n$ questions a student answers correctly $15$ of the first $20$. Of the remaining questions be answers one third correctly. All the questions have the same credit. If the student's mark is $50\%$, how many different values of $n$ can there be?

• A. $50$
• B. $40$
• C. $20$
• D. $100$
• E. the problem cannot be solved

Answer 1

The correct option is A $50$

Total number of questions $=n$

out of first $20$ questions, $15$ questions are marked correctly.

$\therefore$ remaining questions $=(n-20)$

since$\frac{1}{3}rd$ of remaining questions are answered correctly

$\therefore$ no of correct answer $=\frac{1}{3}(n-20)$

since all questions are having same score

$50$ % marks$=50$% questions marked correctly.

$\therefore \frac{15+\frac{(n-20)}{3}}{n}=\frac{50}{100}\Rightarrow 15+\frac{1}{3}(n-20)=\frac{n}{2}\Rightarrow 30+\frac{2}{3}(n-20)=n\Rightarrow 90+2(n-20)=3n\Rightarrow 90+2n-40=3n\Rightarrow n=50$

Hence${}^{\prime }{n}^{\prime }$ has one unique value.