Multiple choice

In an exam, the average score of the candidates was found to be 60. After deducting computational errors, the scores of 100 candidates had to be changed from 80 to 50 each, and the overall average score of students had to be reduced by 10. What was the total number of students in the class?

  1. 300

  2. 400

  3. 500

  4. 600

  5. 800
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A Correct answer
Explanation

Let N be the number of students. Initial sum = 60N. New sum = 60N - 100*(80-50) = 60N - 3000. New average = (60N - 3000)/N = 60 - 10 = 50. 60N - 3000 = 50N, so 10N = 3000, N = 300.

AI explanation

Let the total number of students be N. Reducing 100 scores from 80 to 50 creates a total decrease of 100 multiplied by 30, which is 3000. This 3000 decrease causes the overall average to drop by 10, meaning 10 multiplied by N equals 3000. Solving for N gives a total of 300 students.

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