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    Question

    A group consists of a certain number of individuals. If two

    members, each weighing 59 kg, leave the group, the average weight of the remaining members decreases by 1 kg. Alternatively, if three members, each weighing 60 kg, leave the group, the average weight of the remaining members decreases by 2 kg. Determine the total number of individuals initially present in the group.
    A 10 Correct Answer Incorrect Answer
    B 8 Correct Answer Incorrect Answer
    C 12 Correct Answer Incorrect Answer
    D 14 Correct Answer Incorrect Answer

    Solution

    Let the number of people in group and average weight of group be 'n' and 'm' kg, respectively.
    So, mn - 2 X 59 = (n - 2) X (m - 1)
    Or, mn - 118 = mn - n - 2m + 2
    Or, 2m + n = 120 --------- (I)
    And, mn - 3 X 60 = (n - 3) X (m - 2)
    Or, mn - 180 = mn - 2n - 3m + 6
    Or, 2n + 3m = 186 --------(II)
    On solving 3 X equation I - 2 X equation II,
    We get, 3 X (2m + n) - 2 X (2n + 3m) = 3 X 120 - 2 X 186
    Or, 6m + 3n - 4n - 6m = 360 - 372
    Or, 'n' = 12

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