Question

The average age of 5 boys is 9 years and when their father is included, their average
age is 16 yrs. What is their father's age?​

Answer 1

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ age \ of \ their \ father \ is \ 51 \ years.}$

$\sf\orange{Given:}$

$\sf{\implies{The \ average \ of \ 5 \ boys \ is \ 9 \ years.}}$

$\sf{\implies{When \ their \ father \ in \ included}}$

$\sf{their \ average \ age \ is \ 15 \ years.}$

$\sf\pink{To \ find:}$

$\sf{Their \ father's \ age.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\boxed{\sf{Average=\frac{Sum \ of \ observations}{Number \ of \ observation}}}$

$\sf{According \ to \ the \ first \ condition}$

$\sf{\frac{Sum \ of \ ages \ of \ 5 \ boys}{5}=9}$

$\sf{\therefore{Sum \ of \ ages \ of \ 5 \ boys=9\times5}}$

$\sf{\therefore{Sum \ of \ ages \ of \ 5 \ boys=45...(1)}}$

$\sf{According \ to \ the \ second \ condition.}$

$\sf{\frac{(Sum \ of \ age \ of \ 5 \ boys)+Father's \ age}{6}=16}$

$\sf{...from (1)}$

$\sf{\therefore{\frac{45+Father's \ age}{6}=16}}$

$\sf{\therefore{45+Father's \ age=16\times6}}$

$\sf{\therefore{45+Father's \ age=96}}$

$\sf{\therefore{Father's \ age=96-45}}$

$\sf{\therefore{Father's \ age=51 \ years.}}$

$\sf\purple{\tt{\therefore{The \ age \ of \ their \ father \ is \ 51 \ years.}}}$