Discussion
The average age of three employees is 16 years and their ages are in proportion 2:4:6 What is the age in years of the youngest employee?
Answer: C
The youngest employee is 8 years old. The total of the three ages is \(3\times 16 = 48\) years. The ages are in the ratio 2 : 4 : 6, which makes 12 parts, so one part is \(48 \div 12 = 4\) years. The youngest has 2 parts: \[ 2\times 4 = 8\text{ years} \] The ages are 8, 16 and 24, which add to 48. The 18 years and 10 years answers do not match any share, and 5 years would need a part of 2.5, which gives a total of 30, not 48.
As a check, 8 : 16 : 24 reduces to 1 : 2 : 3, the same as 2 : 4 : 6, and the mean of 8, 16 and 24 is 16.
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