Question

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?

• A. 25
• B. 28
• C. 30
• D. 32

Hint:

When solving average-related problems, first calculate the total sum and then use the corrected values to find the number of students.

Answer 1

The Correct Option is C

Let the number of students be \( n \).
The sum of the marks originally entered was \( 30.8n \).
After correcting the marks, the sum becomes: \[ 30.8n + 42 - 24 = 31.4n. \] Solving the equation: \[ 30.8n + 18 = 31.4n \quad \Rightarrow \quad 18 = 0.6n \quad \Rightarrow \quad n = \frac{18}{0.6} = 30. \] Thus, the class has 30 students.