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The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.

Correct answer: C. 25

  • A. 20
  • B. 15
  • C. 25
  • D. 35

Explanation

Let n be the original number of students. The original total is 80n marks, while the five excluded students contributed 5 × 40 = 200 marks. The remaining total is 90(n - 5) marks, so 80n - 200 = 90n - 450, giving n = 25 students. The likely mistake is choosing 20 students by using the difference between the two averages without accounting for the five excluded students.

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About Averages

An average represents the total of a set of values divided by the number of values, and a weighted average gives different importance to different groups. Problems involve missing values, combined averages, replacement of observations, and changes in the average, so the total and count must be tracked separately.

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