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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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