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)
Explanation
Fixing the wrong entry raises the class total by \(42 - 24 = 18\) marks, and this raises the average by \(31.4 - 30.8 = 0.6\). If the class has \(n\) students, the average rises by \(\frac{18}{n}\), so \(\frac{18}{n} = 0.6\) and \(n = 30\). Check: \(30 \times 30.8 = 924\) and \(924 + 18 = 942 = 30 \times 31.4\).
Answer: C