Mathematics
Grey Kangaroo
2023
20

20

There were twice as many children as adults sitting round a table. The age of each person at the table was a positive integer greater than 1. The sum of the ages of the adults was 156. The mean age of the children was 80% less than the mean age of the whole group. What the sum of the ages of the children?

A 10 B 12 C 18 D 24 E 27

Answer

D

SOLUTIOn

Let the number of adults be n and let the total of the ages of the children be T. The information in the question tells us that the mean age of the children is 20% or 1 5 of the mean age of the whole group. Therefore 1/5 × (156+T)/3n = T/2n . Therefore 2(156 + T) = 3 × 5T and hence 312 = 13C. This has solution T = 24.

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