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

1 thought on “:. The average age of 10 boys is 12<br />years. If a teacher is added to this<br />group, then the average increases to<br />15 ye”

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

   [tex] \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) }} \\ [/tex]

   ~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.

   [tex] \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}}}} \\ [/tex]

   Hence,

   The age of the Teacher will be 45 years.

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