Multiple choice

In a wildlife research centre, the average weight of recorded elephant groups increases by 1.6 quintals when a new group of young elephants is added to the data. If the average weight of the young elephant group is 4 quintals more than that of the average weight of the older elephant groups, what is the ratio of the number of older elephant groups to the number of young elephant groups?

  1. 2 : 5

  2. 3 : 2

  3. 3 : 4

  4. 5 : 3

  5. a
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let N1, A1 be the number and average of older groups, and N2, A2 be for the new group. (N1*A1 + N2*A2) / (N1 + N2) = A1 + 1.6. Given A2 = A1 + 4. Substituting: N1*A1 + N2*(A1 + 4) = (N1 + N2)(A1 + 1.6). N1*A1 + N2*A1 + 4*N2 = N1*A1 + 1.6*N1 + N2*A1 + 1.6*N2. 2.4*N2 = 1.6*N1. N1/N2 = 2.4/1.6 = 3/2.

AI explanation

Using the method of alligation or balance, let the average weight of the older elephant groups be Y and the number of young elephant groups be N. Since the young group's average is Y plus 4, the total increase in sum is N times (Y plus 4) minus N times Y, equaling 4N. The overall average increased by 1.6 quintals, meaning the total increase across all groups must be 1.6 times the combined total number of groups, so 4N equals 1.6 times (the number of older groups plus N). Simplifying 4N equals 1.6 times older groups plus 1.6N gives 2.4N equals 1.6 times the older groups, resulting in a ratio of older groups to young groups of 2.4 divided by 1.6, which is 3:2.

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