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    Question

    A group contains some number of members. If 2 members

    with an average weight of 61 kg leave the group, the average weight of the remaining members decreases by 1 kg. If 3 members with an average weight of 62 kg leave the group, the average weight of the remaining members decreases by 2 kg. Find the number of members initially in the group.
    A 12 Correct Answer Incorrect Answer
    B 18 Correct Answer Incorrect Answer
    C 10 Correct Answer Incorrect Answer
    D 15 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the number of members in group and average weight of group be 'n' and 'm' kg, respectively.

    So,

    mn - 2 × 61 = (n - 2) × (m - 1)

    Or, mn - 122 = mn - n - 2m + 2

    Or, 2m + n = 124 --------- (I)

    And,

    mn - 3 × 62 = (n - 3) × (m - 2)

    Or, mn - 186 = mn - 2n - 3m + 6

    Or, 2n + 3m = 192 -------- (II)

    On solving 3 × equation (I) - 2 × equation (II),

    We get, 3 × (2m + n) - 2 × (2n + 3m) = 3 × 124 - 2 × 192

    Or, 6m + 3n - 4n - 6m = 372 - 384

    Or, -n = -12

    Thus, 'n' = 12

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