Question-23

algebra
aptitude

The average marks obtained by a class in an examination were calculated as 30.8. However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as 24 instead of 42. After correcting the marks, the average becomes 31.4.

How many students does the class have?

Let the class have \(\displaystyle n\) students. The incorrect sum of the marks of all students is \(\displaystyle 30.8n\). The correct sum is \(\displaystyle 30.8n-24+42=30.8n+18\). The average is now \(\displaystyle 31.4\):

\[ \begin{aligned} \frac{30.8n+18}{n} & =31.4\\ 0.6n & =18\\ n & =30 \end{aligned} \]