Multiple choice

The average marks obtained by a student in some tests is 15. On re-appearing for first and last test, his score improved in first test by 30 but it reduced by 5 marks in last test. Due to which, his average improved and became 17.5. Find the total number of tests in which he appeared.

  1. 20

  2. 18

  3. 15

  4. 10
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D Correct answer
Explanation

Let n be the number of tests. Initial sum = 15n. New sum = 15n + 30 - 5 = 15n + 25. New average = (15n + 25)/n = 17.5. 15n + 25 = 17.5n, so 2.5n = 25, n = 10.

AI explanation

The net improvement in total marks is found by multiplying the change in average by the number of tests, so 2.5 times the number of tests gives the total mark increase. The student gained 30 marks on the first test but lost 5 marks on the last test, making the net improvement 30 minus 5, which is 25 marks. Setting the total mark increase equal to this net improvement gives 2.5 times the number of tests equals 25. Dividing 25 by 2.5 reveals that the total number of tests is 10.

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