Multiple choice

In a Science fair competition, there are 50 participants consisting of students and teachers. The average score of the students is 75 points, while the average score of the teachers is 85 points. If the overall average score of the participants is 78 points, what is the ratio of the number of students to the number of teachers in the competition?

  1. 4 : 7

  2. 3 : 4

  3. 7 : 3

  4. 4 : 3
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C Correct answer
Explanation

Let S be the number of students and T be the number of teachers. Using the weighted average formula: (75S + 85T) / (S + T) = 78. This simplifies to 75S + 85T = 78S + 78T, or 7T = 3S, so S/T = 7/3.

AI explanation

Using the method of alligation on the average scores, the ratio of students to teachers equals the difference between the teacher average and the overall average divided by the difference between the overall average and the student average. This gives (85 minus 78) divided by (78 minus 75), which is 7 divided by 3. Therefore, the ratio is 7 : 3.

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