Question

In a class, in an examination in Mathematics, $10$ students scored $100$ marks each, $2$ students scored zero and the average of the remaining students is $72$ marks. If the class average is $76$, then the number of students in the class is

• A. $44$
• B. $40$
• C. $38$
• D. $34$
• E. $32$

Answer 1

The correct option is D $34$

Let be the remaining the number of students in the class$=n$
Then, total marks of students
$=(10\times 100)+(2\times 0)+72n=1000+72n$
According to the question
$\frac{1000+72n}{n+12}=76$ ($\because$ total student $=n+12$)
$1000+72n=76n+76\times 12$
$1000-912=76n-72n$
$\Rightarrow 4n=86\Rightarrow n=\frac{88}{4}=22$
$\therefore$ Total number of students$=22+12=34$