Question

:. The average age of 10 boys is 12
years. If a teacher is added to this
group, then the average increases to
15 years. The age of the teacher is.​

Answer 1

• Average age of 10 boys is 12 years
• If a teacher is added to this group, then the average increases to 15 years.

$\colon\implies{\sf{ 12 = \dfrac{ ( x_1,x_2 \cdots x_{10} )}{10} }} \\ \\ \\ \colon\implies{\sf{ 120 = ( x_1,x_2 \cdots x_{10} ) \ \ \ \ \ \cdots(1) }}$

~Now, we've to find the 2nd condition as to find the age of the teacher so:-

Let the age of the Teacher be x.

$\circ \ {\pmb{\underline{\sf{ According \ to \ Question: }}}} \\ \\ \\ \colon\implies{\sf{ 15 = \dfrac{ ( x_1,x_2 \cdots x_{10} ) + x}{11} }} \\ \\ \\ \colon\implies{\sf{ 165 = ( x_1,x_2 \cdots x_{10} ) + x }} \\ \\ \\ \colon\implies{\sf{ 165 = 120 + x \ \ \ \ \ \ \ [using \ (1)] }} \\ \\ \\ \colon\implies{\sf{ 165 - 120 = x }} \\ \\ \\ \colon\implies{\underline{\boxed{\sf\red{ x = 45 \ years}}}}$

Hence,

The age of the Teacher will be 45 years.