Question

The average age of 5 children in a family is 10 years .if the age of four of them are 12,14,15 and 8years what is the age of fifth child?

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Age\:of\:fifth\:child=1\:years}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green {\underline \bold{given :}} \\ \tt{: \implies Average \: age \: of \: 5 \: children = 10 \: years} \\ \\ \tt{: \implies Age \: of \: four \: children =(12,14,15 \: and \: 8)\:years} \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt{: \implies Age \: of \: fifth \: child =?}$

• According to given question :

$\bold{ \circ \: As \: we \: know \: that} \\ \\ \tt{: \implies \frac{Total \: age \: of \: 5 \: children}{Total \: number \: of \: children } =10} \\ \\ \circ \: \text{Putting \: given \: values} \\ \\ \tt{: \implies \frac{12 + 14 + 15 + 8 + Age \: of \: fifth \: child}{5} = 10} \\ \\ \circ \: \text{Let \: age \: of \: 5th \: child} \\ \tt{: \implies \frac{49 + x}{5} = 10} \\ \\ \tt{: \implies 49 + x = 50} \\ \\ \tt{: \implies x = 50 - 49} \\ \\ \green{\tt{: \implies x = 1 \: years}} \\ \\ \green{\tt{ \therefore Age \: of \: fifth \: child \: is \: \: 1 \: years}}$

Answer 2

Answer:

$\large{\underline{\boxed{\mathfrak\blue{Age \: of \: 5th \: child = 1 \: year }}}}$

Given:-

1. Average age of 5 children = 10 years.
2. Ages of 4 children = 12,14,15 & 8

To find:-

• Age of 5th children = ?

$\rm We \: know, \\\\\star \: \large{\boxed{\sf\purple{Average \: age = \dfrac{Total \: age }{Number \: of \: people} }}}$

Let the age of 5th children be x years.

• Number of children = 5

$\rm Now, \\\\\Rightarrow\rm 10 = \dfrac{12 + 14 + 15 + 8 + x}{5} \\\\\Rightarrow\rm 10 = \dfrac{49 + x}{5} \\\\\Rightarrow\rm 10 \times 5 = 49 + x \\\\\Rightarrow\rm 50 = 49 + x \\\\\Rightarrow\rm x = 50 - 49 \\\\\Rightarrow\rm x = {\boxed{\rm{1 \: year }}}$

${\underline{\therefore{\rm{Age \: of \: 5th \: child = 1 \: year }}}}$

$\rule{200}{1}$

${\underline{\underline{\sf\green{Verification:- }}}}$

$\Rightarrow\rm \dfrac{Total \: ages}{Number \: of \: children} = Average \: age \\\\\Rightarrow\rm \dfrac{12 + 14 + 15 + 8 + 1}{5} = 10 \\\\\Rightarrow\rm \dfrac{50}{5} = 10 \\\\\Rightarrow\rm 10 = 10 \: \: \: \:[Proved!]$

${\underline{\underline{\therefore{\text{Age \: of \: 5th \: child = 1 \: year }}}}}$