Question
The average score obtained by 26 students in a class
test is 68 marks. The top place was shared by 3 people who got the same score. If the lowest score was 40 marks, then which of the following could be the highest score obtained by toppers? (Marks scored by each student is a whole number)Solution
To maximize the toppers score, we must minimize the scores of everyone else. So, let the scores of other 23 students be 40 marks each. So, total marks obtained by 23 students = 40 x 23 = 920 Remaining marks = 1768 - 920 = 848 So, score of toppers = 848 ÷ 3 = 282 marks + 2 additional mark This additional mark could be obtained by any other student.
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