The average marks of 40 students in a class is 59 and after removing the highest mark, the average of the remaining 39 students is 58. What is the highest mark in the class ?
98
99
97
100
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CISF-AC-EXE – 2021
Number of students initially = 40
Average marks of 40 students = 59
Total marks of 40 students = Average $\times$ Number of students
Total marks (40 students) = $59 \times 40$.
$59 \times 40 = 2360$.
After removing the highest mark:
Number of remaining students = 39
Average marks of 39 students = 58
Total marks of 39 students = Average $\times$ Number of students
Total marks (39 students) = $58 \times 39$.
$58 \times 39 = 58 \times (40 – 1) = 58 \times 40 – 58 \times 1 = 2320 – 58 = 2262$.
The highest mark is the difference between the total marks of 40 students and the total marks of the remaining 39 students.
Highest mark = Total marks (40 students) – Total marks (39 students)
Highest mark = $2360 – 2262$
Highest mark = 98.