From the given average age of three persons, the age of the youngest one among them is equal to [tex]9[/tex] years.
What is average?
" Average is defined as the ratio of the sum of all the given quantity to the number of given quantity."
Formula used
Average [tex]= \ \frac { 1 }{n} \sum _ { } { } x_ {i} \)[/tex]
[tex]n=[/tex] number of given quantity
[tex]\sum_{}{}x_{i} =[/tex] sum of all the given quantity
According to the question,
Number of persons [tex]= 3[/tex]
Average ages of three person [tex]= 27[/tex]
Substitute the value in the formula we get,
[tex]27 = \frac{\sum _ {}{}x_{i}}{3}\\ \\\implies \sum _ {}{}x_{i}}= 27 \times 3\\\\\implies \sum _ {}{}x_{i}}= 81[/tex]
Proportion of the ages of three person [tex]= 1: 3: 5[/tex]
[tex]'x'[/tex] represents the age
As per given condition of average age we get,
[tex]x + 3x + 5x = 81\\\\\implies 9x = 81\\\\\implies x = 9[/tex]
Age of first person [tex]1x = 9 \ years[/tex]
Age of second person [tex]3x = 27 \ years[/tex]
Age of third person [tex]5x =45 \ years[/tex]
Hence ,as per given average age of youngest person is equal to [tex]9 \ years[/tex].
Learn more about average here
brainly.com/question/27646993
#SPJ2
