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The average score of student in an exam is 90 if the scores of the top 5 students are not considered then the average remaining drops by 5 if the second ranker scored less than 140 and all the students got intergal scores find the minimum marks that could have been scored by the topper?
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The average score of student in an exam is 90 if the scores of the top...
Problem: Find the minimum marks that could have been scored by the topper in an exam given the average score of students is 90, the average drops by 5 if the scores of the top 5 students are not considered, and all the students scored integer marks.
Solution:
To solve this problem, we need to use the concept of weighted average.
Solution:
To solve this problem, we need to use the concept of weighted average.
- Find the average score of the top 5 students:
- Find the average score of remaining students:
- Find the minimum marks scored by the topper:
Let the scores of the top 5 students be a, b, c, d, and e. Then, we have:
Total score of top 5 students = a + b + c + d + e
Average score of top 5 students = (a + b + c + d + e)/5
Since we don't know the exact scores of the top 5 students, we can assume that they scored the maximum possible integer marks. Therefore, we have:
a = b = c = d = e = 100.
Total score of top 5 students = 500
Average score of top 5 students = 100
Let the number of remaining students be n. Then, we have:
Total score of remaining students = 90 * n
Average score of remaining students = 90
If we exclude the top 5 students, then the number of remaining students becomes n - 5. Let the new average score of remaining students be x. Then, we have:
Total score of remaining students = x * (n - 5)
Average score of remaining students = x
We are given that the average drops by 5 if the top 5 scores are not considered. Therefore, we have:
x = 85
Total score of remaining students = 85 * (n - 5)
Let the minimum marks scored by the topper be m. Then, we have:
Total score of all students = 90 * (n + 5)
Total score of all students = m + 500 + 85 * (n - 5)
Since all the students scored integer marks, the total score of all students must be an integer. Therefore, we have:
m + 500 + 85 * (n - 5) = 90 * (n + 5)
Simplifying the above equation, we get:
m = 445 + 5n
To find the minimum value of m, we need to find the minimum value of n. Since all the students scored integer marks, the minimum value of n must be such that 85 * (n - 5) is a multiple of 90. Therefore, we have:
n - 5 = 18
n = 23
Substituting n = 23 in the above equation, we get:
m = 550
Therefore, the minimum marks that could have been scored by the topper is 550.
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The average score of student in an exam is 90 if the scores of the top 5 students are not considered then the average remaining drops by 5 if the second ranker scored less than 140 and all the students got intergal scores find the minimum marks that could have been scored by the topper?
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The average score of student in an exam is 90 if the scores of the top 5 students are not considered then the average remaining drops by 5 if the second ranker scored less than 140 and all the students got intergal scores find the minimum marks that could have been scored by the topper? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The average score of student in an exam is 90 if the scores of the top 5 students are not considered then the average remaining drops by 5 if the second ranker scored less than 140 and all the students got intergal scores find the minimum marks that could have been scored by the topper? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average score of student in an exam is 90 if the scores of the top 5 students are not considered then the average remaining drops by 5 if the second ranker scored less than 140 and all the students got intergal scores find the minimum marks that could have been scored by the topper?.
The average score of student in an exam is 90 if the scores of the top 5 students are not considered then the average remaining drops by 5 if the second ranker scored less than 140 and all the students got intergal scores find the minimum marks that could have been scored by the topper? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The average score of student in an exam is 90 if the scores of the top 5 students are not considered then the average remaining drops by 5 if the second ranker scored less than 140 and all the students got intergal scores find the minimum marks that could have been scored by the topper? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average score of student in an exam is 90 if the scores of the top 5 students are not considered then the average remaining drops by 5 if the second ranker scored less than 140 and all the students got intergal scores find the minimum marks that could have been scored by the topper?.
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