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
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Explanatory Answer
he arithmetic mean of the scores of 25 students = 50
Sum of scores of these students = 25 × 50 = 1250
For the scores of the top 5 students to be as high as possible, the score of the bottom 20 students should be as low as possible.
The minimum score is 30, and the scores of the bottom 20 students are distinct integers.
In order for the bottom 20 scores to be as low as possible, they must be,
30, 31, 32, … 49
Sum of the bottom 20 scores
= 30 + 31 + 32 + … + 49
= (30 + 0) + (30 + 1) + (30 + 2) + … + (30 + 19)
= 20 × 30 + (0 + 1 + 2 + 3 + … + 19)
= 600 + 
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