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A student's marks were incorrectly entered as 45 instead of 60. Due to this, the average marks of the class increased by 0.5. What is the number of students in the class?
20
25
30
35
30
Simply find the total error (60 - 45 = 15) and divide it by the observed increase in average (0.5). Thus, 15/0.5=30.
Original incorrect marks entered = 45, Actual marks = 60, Average increase = 0.5.
Number of students=Change in averageDifference in sum of marks
Simply find the total error (60 - 45 = 15) and divide it by the observed increase in average (0.5). Thus, 15/0.5=30.
Many students try to calculate the total sum before and after, but often forget that the 'increase in average' applies to every single student in the class.
Calculate the total error
Determine the difference between the actual marks and the entered marks.
60−45=15
Relate total error to the average change
Since the total change in marks is distributed across n students, the change in average is equal to the total difference divided by the number of students.
Change in Average=nTotal Error⇒0.5=n15
Solve for the number of students
Isolate n by dividing the total error by the average increase.
n=0.515=30
C is correct because the total discrepancy of 15 marks when distributed across the class results in an average increase of 0.5 per student, implying 30 students.
This concept of 'total redistribution' is frequently used in weighted average problems and profit/loss distribution questions in competitive exams.