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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 - 3Γ—65 = (n - 3)(m - 1)

      β†’ mn - 195 = mn - 3m - n + 3

      β†’ 3m + n = 198 -------- (i)

      After 4 people leave:

      mn - 4Γ—66 = (n - 4)(m - 2)

      β†’ mn - 264 = mn - 4m - 2n + 8

      β†’ 4m + 2n = 272

      β†’ divide by 2: 2m + n = 136 -------- (ii)

      Now solve equations:

      From (i): n = 198 - 3m

      Substitute into (ii):

      2m + (198 - 3m) = 136

      β†’ 2m + 198 - 3m = 136

      β†’ -m = -62

      β†’ m = 62

      β†’ n = 198 - 3Γ—62 = 198 - 186 = 12

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