Correct Option (B)
The initial total marks for 100 students, with an average of 40, were calculated as 100 × 40 = 4000. It was subsequently identified that a student's marks of 53 were erroneously recorded as 83. To correct the total, the difference between the misread value and the actual value (83 - 53 = 30) must be subtracted from the initial total. Thus, the corrected total marks are 4000 - 30 = 3970. The corrected mean marks are then calculated by dividing the corrected total marks by the number of students: 3970 / 100 = 39.7.
Incorrect Options:
- Option (A) 39: This value would imply a total sum of 3900 (39 × 100), which represents a larger reduction in total marks than the actual correction of 30 marks.
- Option (C) 40: This value represents the original, uncorrected mean. It would be correct only if the identified error had no net impact on the total sum, which is not the case here.
- Option (D) 40.3: This value would imply a total sum of 4030 (40.3 × 100), which suggests an increase in the total marks, contrary to the required correction.