Question

The average score in an examination of 10 students of a class is 60. if the scores of the
top five students are not considered the average score of the remaining students fall
by 5. The pass marks was 40 and the maximum mark was 100.It is also known tha
none of students failed. If each of the top five scorers had distinct integeral scores, th
maximum possible score of the topper is.​

Answer 1

Answer:

Hey mate here is your answer...

If the value of all other except the largest is 55..

Largest will be 60*10-55*9=600-495=105..

However the top 5 are distinct and the smallest of these can be 55, so remaining THREE will be 1,2,&3 more so total combined value will be 1+2+3 or 6 more..

Therefore the largest will be 6 less than max possible..... 105-6=99

Answer 2

Given:

The average score of 10 students in an examination is 60 marks. If the students with the top 5 scores are omitted from the average. The average decreases by 5. The minimum score for clearing the exam is 40. None of the students have failed the exam. None of the 5 top scorers have the same score.

To Find:

The maximum possible score of the topper.

Solution:

The given problem can be solved using the concepts of averages.

1. Let the 10 students be s1, s2, s3, s4, s5, s6, s7, s8, s9, s10. The average score of the 10 students is 60.

=> (s1 + s2 + s3 + s4 + s5 + s6 + s7 + s8 + s9 + s10)/10 = 60,

=>  s1 + s2 + s3 + s4 + s5 + s6 + s7 + s8 + s9 + s10 = 600. ( Assume as equation 1).

2. Let the top 5 scorer students be s6, s7, s8, s9, s10. The average score of the remaining students except the top scorers is 55,

=> (s1 + s2 + s3 + s4 + s5)/5 = 55,

=> s1 + s2 + s3 + s4 + s5 = 275. ( Assume as equation 2)

3. Subtract equation 2 from equation 1,

=> s6 + s7 + s8 + s9 + s10 = 325.

=> Assume s10 has scored the highest among all the students.

=> The least possible scores of s6, s7, s8, s9 are 55, 56, 57, and 57 as the scores are slightly greater than  or equal to the average scores.

=> Hence, the maximum possible score by the topper is,

=> s10 = 325 - 55 - 56 - 57 - 58,

=> marks scored by the topper = 325 - (226),

=> highest possible marks scored by the topper = 99.

Therefore, the maximum possible score of the topper is 99 out of 100.