Multiple choice

The average marks of eight students increase by 21 when a new student comes in place of one of them whose marks were 96. Find the marks of the new student.

  1. 85

  2. 264

  3. 117

  4. 234
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B Correct answer
Explanation

Let the sum of marks be S. New sum = S - 96 + X. New average = (S - 96 + X)/8 = S/8 + 21. X - 96 = 8 * 21 = 168. X = 168 + 96 = 264.

AI explanation

By the method of average increase, the new student must score enough to match the replaced student's marks plus raise the overall total. The total increase needed for the eight students is 8 times 21, which equals 168. Adding this to the replaced student's marks of 96 gives 96 + 168 = 264, the marks of the new student.

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