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      Question

      In a classroom of 45 students, the average height is 150

      cm. One student of height 146 cm leaves, and 3 new students with an average height of 154 cm join. When the teacher is also included, the average height becomes 151 cm. What is the height of the teacher?
      A 178 cm Correct Answer Incorrect Answer
      B 182 cm Correct Answer Incorrect Answer
      C 180 cm Correct Answer Incorrect Answer
      D 176 cm Correct Answer Incorrect Answer
      E 174 cm Correct Answer Incorrect Answer

      Solution

      Initial total height = 45 × 150 = 6750 cm
      Height of 3 new students = 3 × 154 = 462 cm Let the height of the teacher be ‘y’ cm
      New total height without teacher = 6750 - 146 + 462 + y = (7066 + y)
      New total number of people = 45 - 1 + 3 + 1 = 48
      New total height = 48 × 151 = 7248 cm
      So, teacher’s height = 7248 - 7066 = 182 cm

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