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      Question

      The average of 30 numbers is 72. If the average of the

      first 12 numbers is 60 and the average of the last 19 numbers is 80, find the 12th number.
      A 60 Correct Answer Incorrect Answer
      B 55 Correct Answer Incorrect Answer
      C 80 Correct Answer Incorrect Answer
      D 45 Correct Answer Incorrect Answer

      Solution

      ATQ,

      Sum of all 30 numbers = 30 × 72 = 2160

      Let the 12th number be ‘x’

      Sum of first 12 numbers = 12 × 60 = 720

      Sum of last 19 numbers = 19 × 80 = 1520

      Now, 12th number is included in both groups:

      720 + 1520 - x = 2160

      => 2240 - x = 2160

      => x = 2240 - 2160

      => x = 80

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