Multiple choice

The average runs of two groups is $57$. The mean of the first group is $52$ and the mean of the second group is $60$. The proportion of ______.

  1. $3 : 5$
  2. $2 : 5$1
  3. $2 : 8$
  4. $5 : 2$
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A Correct answer
Explanation

Let the group sizes be x and y. Using the weighted mean, 52x + 60y = 57(x + y), which gives 5x = 3y and therefore x:y = 3:5.

AI explanation

Using the method of alligation, the ratio of the number of entities in the two groups is determined by the differences between their individual averages and the combined average. The difference between the second group's average and the combined average is 60 minus 57, which equals 3. The difference between the combined average and the first group's average is 57 minus 52, which equals 5, making the proportion 3 to 5.

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