Multiple choice

A school's Science and Math clubs have different average ages. The average age of students in the Science club is 15 years, while the average age of students in the Math club is 17 years. If the average age of all students in both clubs combined is 16 years, what is the ratio of the number of students in the Science club to the number of students in the Math club?

  1. 1 : 1

  2. 1 : 3

  3. 1 : 2

  4. 2 : 1
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A Correct answer
Explanation

Using the allegation method, the difference between the average ages (15, 17) and the combined average (16) gives the ratio. |17-16| : |15-16| = 1 : 1.

AI explanation

Using the method of alligation, we compare the differences between each club's average and the combined average. The difference for the Science club is 16 - 15 = 1 year, and the difference for the Math club is 17 - 16 = 1 year. The ratio of these differences gives the ratio of students, which is 1:1.

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