Question

8 students appeared in an examination of 100 marks, the topper of the exam got 84 marks and the average marks of all the students were 52.5. If the passing marks were 40 and it is known that no student failed the exam. Find the maximum possible marks of the second topper if the marks of each student is a distinct integral number.
1. 80
2. 81
3. 79
4. 82

Answer 1

Correct Answer - Option 2 : 81

GIVEN:

No of students = 8

Topper's marks = 84

Average marks = 52.5

Passing marks = 40

CONCEPT:

For one candidate's marks to be the maximum possible other's marks have to be the minimum possible.

FORMULA USED:

Average = sum of all observations/total no of observations

CALCULATION:
Total marks = 52.5 × 8 = 420

Total marks of students excluding topper = 420 - 84 = 336

As no student failed minimum marks will be 40 

Also, marks are distinct and integral,

∴ Minimum possible marks of other students = 41, 42, 43, 44, 45

Max possible marks of 2nd topper = 336 - (40 + 41 + 42 + 43 + 44 + 45) = 81

∴ Max possible marks will be 81