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The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers is
Correct answer is '92'. Can you explain this answer?
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The arithmetic mean of scores of 25 students in an examination is 50. ...
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Given Information:
The mean score of 25 students is 50, and 5 students have the same highest score. The lowest score is 30 and the rest are distinct integers.

Calculating Total Score:
Total score of all 25 students = 25 * 50 = 1250

Finding the Total Score of the 5 Toppers:
Let the score of the 5 toppers be x.
Total score of the 5 toppers = 5x

Finding the Total Score of the Rest of the Students:
Total score of the rest of the students = 1250 - 5x - 30 (subtracting the lowest score)

Determining the Scores of the Rest of the Students:
Since the scores of the rest of the students are distinct integers, the highest possible score for the rest of the students can be 91 (30, 31, 32, 33, 34, ..., 91). Any score higher than 91 will result in duplicate scores.

Calculating the Maximum Possible Score of the Toppers:
Maximum possible score of the toppers = Total score of the toppers - Total score of the rest of the students
= 1250 - 91 - 30
= 1229
Therefore, the maximum possible score of the toppers is 92.
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Community Answer
The arithmetic mean of scores of 25 students in an examination is 50. ...
Let sum of marks of students be x
Now therefore x = 25*50 =1250
Now to maximize the marks of the toppers
We will minimize the marks of 20 students
so their scores will be (30,31,32.....49 )
let score of toppers be y

we get 5y +790=1250
5y=460
y=92
So scores of toppers = 92
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The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers isCorrect answer is '92'. Can you explain this answer?
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