Discussion
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?
Answer: C
The class has 30 students.
Correcting the entry from 24 to 42 adds 18 marks to the total, and this raises the average from 30.8 to 31.4, an increase of 0.6. If there are \(n\) students,
\[ \begin{aligned} \frac{18}{n} &= 31.4 - 30.8 = 0.6 \\ n &= \frac{18}{0.6} = 30 \end{aligned} \]
Check: \(30 \times 30.8 = 924\), and \(924 + 18 = 942 = 30 \times 31.4\). With 25, 28 or 32 students the extra 18 marks would raise the average by 0.72, about 0.64 or about 0.56, not 0.6.
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