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A student's marks were incorrectly entered as 34 instead of 70. Due to this, the average marks of the class got decreased by 34. What is the number of students in the class?
28
32
27
23
28
Calculate the total discrepancy (70 - 34 = 36) and divide it by the change in average (4/3). Thus, 36 / (4/3) = 36 * 3 / 4 = 27.
Correct marks = 70, Incorrect marks = 34, Decrease in average = 4/3
n=Change in averageDifference in marks
Calculate the total discrepancy (70 - 34 = 36) and divide it by the change in average (4/3). Thus, 36 / (4/3) = 36 * 3 / 4 = 27.
Students often subtract 70 from 34 to get -36, forgetting that the magnitude of the total change is what dictates the shift in average.
Calculate the difference in marks
Find the absolute difference between the correct and incorrect marks to determine the total impact on the sum of scores.
36=70−34
Apply the average formula relationship
Since the total change in the sum of marks is equal to the number of students (n) multiplied by the change in average (ΔA), we rearrange the formula to find n.
n=4/336
Solve for the number of students
Multiply the numerator by the reciprocal of the fraction to isolate the number of students.
n=36×43=9×3=27
C is correct because the calculation of total difference (36) divided by the average decrement (4/3) results in 27 students.
This concept of 'Total Change = Difference per unit × Number of units' is identical to solving problems on displacement of average weights or ages, often seen in RRB exams.
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