Multiple choice

In an examination, the average marks of all students was 72. After correcting mistakes, the average marks of 40 students decreased from 80 to 60, while the marks of the remaining students remained unchanged. As a result, the overall average of all students became 70. Find the total number of students.

  1. 450

  2. 410

  3. 428

  4. 400

  5. 475
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D Correct answer
Explanation

Let N be the total students. Initial sum = 72N. New sum = 72N - 40(80-60) = 72N - 800. New average = (72N - 800)/N = 70. 72N - 800 = 70N -> 2N = 800 -> N = 400.

AI explanation

Let the total number of students be N, so the initial total marks were 72 times N. The average marks of 40 students decreased from 80 to 60, meaning their total marks dropped from 3200 to 2400, a reduction of 800 marks. Because the marks of the remaining students were unchanged, this 800-mark reduction caused the new overall total to be 70 times N. Setting up the equation 72N minus 800 equals 70N gives 2N equals 1600, which means the total number of students is 400.

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