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

To solve this problem, we need to find the total number of students in the class using the given information about averages and corrections to the marks.

1. Let's assume the number of students in the class is n.
2. According to the problem, the average marks calculated initially were 30.8, which means the total sum of marks initially recorded can be expressed as:
   S = n \times 30.8
3. It was found that one student's marks were entered incorrectly as 24 instead of 42. This means the actual total sum of the marks should be:
   S_{\text{actual}} = S + (42 - 24) = n \times 30.8 + 18
4. After correcting the marks, the new average becomes 31.4, which leads to:
   \frac{S_{\text{actual}}}{n} = 31.4
5. Substitute the expression for S_{\text{actual}} from step 3:
   \frac{n \times 30.8 + 18}{n} = 31.4
6. Multiply both sides by n to remove the fraction:
   n \times 30.8 + 18 = n \times 31.4
7. Rearranging gives:
   18 = n \times 31.4 - n \times 30.8
8. Simplifying further, we find:
   18 = n \times (31.4 - 30.8) = n \times 0.6
9. Solving for n gives:
   n = \frac{18}{0.6} = 30

Therefore, the number of students in the class is 30.

The correct answer is, therefore, 30.