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    Question

    In a company team, if 3 employees each weighing 65 kg

    resign, the average weight of the remaining team members drops by 1 kg. But if 4 employees with an average weight of 66 kg resign, the average weight reduces by 2 kg. What was the original number of employees in the team?
    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,

    Let the total number of employees = n, and average weight = m

    After 3 people leave:

    mn - 3×65 = (n - 3)(m - 1)

    → mn - 195 = mn - 3m - n + 3

    → 3m + n = 198 -------- (i)

    After 4 people leave:

    mn - 4×66 = (n - 4)(m - 2)

    → mn - 264 = mn - 4m - 2n + 8

    → 4m + 2n = 272

    → divide by 2: 2m + n = 136 -------- (ii)

    Now solve equations:

    From (i): n = 198 - 3m

    Substitute into (ii):

    2m + (198 - 3m) = 136

    → 2m + 198 - 3m = 136

    → -m = -62

    → m = 62

    → n = 198 - 3×62 = 198 - 186 = 12

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