Question

The average age of the boys in a class is ten years. The average age of girls in the class is eight years.
There are 50% more boys than girls in the class. Find the average age of the class (in years).
a) 8.4 b) 8.8 c) 9.2 d) 9.6

Answer 1

Let the Number of Girls in the class be : n

Given : There are 50% more Boys than Girls in the class.

$:\implies$  Number of Boys in the Class = [n + (50% × n)]

$:\implies \mathsf{Number\;of\;Boys\;in\;the\;Class = \bigg(n + \dfrac{50}{100} \times n\bigg)}$

$:\implies \mathsf{Number\;of\;Boys\;in\;the\;Class = \bigg(n + \dfrac{n}{2}\bigg)}$

$:\implies \mathsf{Number\;of\;Boys\;in\;the\;Class = \dfrac{3n}{2}}$

Given : Average age of Boys in the class = 10 years

We know that :

$\bigstar\;\;\boxed{\mathsf{Average = \dfrac{Sum\;of\;all\;Observations}{Total\;Number\;of\;Obeservations}}}$

$\bigstar\;\;\mathsf{Average\;age\;of\;Boys = \dfrac{Sum\;of\;the\;ages\;of\;all\;Boys}{Total\;Number\;of\;Boys}}$

$\mathsf{\implies \dfrac{Sum\;of\;the\;ages\;of\;all\;Boys}{\dfrac{3n}{2}} = 10}$

$\mathsf{\implies Sum\;of\;the\;ages\;of\;all\;Boys = \bigg(10 \times \dfrac{3n}{2}\bigg)}$

$\mathsf{\implies Sum\;of\;the\;ages\;of\;all\;Boys = 15n}$

Given : Average age of Girls in the class = 8 years

$\bigstar\;\;\mathsf{Average\;age\;of\;Girls = \dfrac{Sum\;of\;the\;ages\;of\;all\;Girls}{Total\;Number\;of\;Girls}}$

$\mathsf{\implies \dfrac{Sum\;of\;the\;ages\;of\;all\;Girls}{n} = 8}$

$\mathsf{\implies Sum\;of\;the\;ages\;of\;all\;Girls = 8n}$

$\bigstar\;\;\mathsf{Average\;age\;of\;the\;class = \dfrac{Sum\;of\;the\;ages\;of\;all\;Boys\;and\;Girls}{Total\;Number\;of\;Students}}$

$\implies \mathsf{Average\;age\;of\;the\;class = \dfrac{15n + 8n}{\bigg(n + \dfrac{3n}{2}\bigg)}}$

$\implies \mathsf{Average\;age\;of\;the\;class = \dfrac{23n}{\bigg(\dfrac{5n}{2}\bigg)}}$

$\implies \mathsf{Average\;age\;of\;the\;class = \dfrac{46}{5}}$

$\implies \mathsf{Average\;age\;of\;the\;class = 9.2}$

Answer 2

Answer:

9.2

Step-by-step explanation:

The average age of girls in the class is eight years.

There are 50% more boys than girls in the class. Find the average age of the class (in years).