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    Question

    In a tournament, the average

    score of eight batsmen in the Chennai team is 80. If the highest three scores are not considered, the new average of the remaining players decreases by four. Assuming that the top four scores are all distinct whole numbers, what is the maximum score possible for any of these batsmen?
    A 65 Correct Answer Incorrect Answer
    B 120 Correct Answer Incorrect Answer
    C 105 Correct Answer Incorrect Answer
    D 95 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Total score of 8 batsmen = 8×80 = 640 Average of the bottom five batsmen = 80 - 4 = 76 Total score of the bottom five batsmen = 5×76 = 380 Total score of the top three batsmen = 640 − 380 = 260 To maximize one player’s score, we keep the other scores at their minimum possible. Possible scores for the top three could be 77, 78, and a maximum score of 105.

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