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    Question

    In a group, 2 people with average weight 55 kg leave,

    and the average drops by 1 kg. If 3 people of average weight 56 kg leave, average drops by 2 kg. Find original number of people.
    A 10 Correct Answer Incorrect Answer
    B 12 Correct Answer Incorrect Answer
    C 15 Correct Answer Incorrect Answer
    D 21 Correct Answer Incorrect Answer

    Solution

    ATQ,
    mn - 110 = (n - 2)(m - 1)

    → mn - 110 = mn - n - 2m + 2

    → n + 2m = 112 -------- (i)

    mn - 168 = (n - 3)(m - 2)

    → mn - 168 = mn - 2n - 3m + 6

    → 2n + 3m = 174 -------- (ii)

    Multiply (i) by 2: 2n + 4m = 224

    Subtract (ii):

    2n + 4m - 2n - 3m = 224 - 174

    → m = 50

    → n = 112 - 2×50 = 12

    Hence, answer is 12 people

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