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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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