Multiple choice

The average of the test scores of a class of m students is 70 and that of n students is 91. When the scores of both the classes are combined, the average is 80. What is n/m

  1. 11/10

  2. 13/10

  3. 10/13

  4. 10/11
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D Correct answer
Explanation

Total score = 70m + 91n = 80(m + n). 70m + 91n = 80m + 80n. 11n = 10m. So n/m = 10/11.

AI explanation

Using the method of alligation, write the average difference for the first class as 80 minus 70 to give 10, and the average difference for the second class as 91 minus 80 to give 11. This establishes the ratio of students in the first class to the second class as 11 is to 10. The requested ratio of n to m is the inverse of this proportion, resulting in 10/11.

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