Question

the average age of 12 girls in a class is 22years and of the ,18 boys in the class 24 years the average age of class is​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Average age of the class is 23.2 years.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Total Girls = 12

Average age = 22 years

Total boys = 18

Average age = 24 years

To Find :

The average age of the class

Solution :

First find the total sum of the age of the girls.

Consider the sum of Girls' Ages as x

• Sum of Observations = x
• Number of Observations = 12
• Average age = 22

★ Mean = $\boxed{\sf{\frac{Sum \: of \: Observations}{No. \: of \: Observations}}}$

$\sf{\longrightarrow} \:22 = \dfrac{x}{12}$

$\sf{\longrightarrow} \:x = 12 \times 22$

$\sf{\longrightarrow} \:x = 264$

Sum of the Ages of the girls = 264 years.

$\rule{300}{1.5}$

Find the total sum of the Boys' Ages -

Consider the sum of ages as x

• Sum of Observations = x
• Number of Observations = 18
• Average age = 24

★ Mean = $\boxed{\sf{\frac{Sum \: of \: Observations}{No. \: of \: Observations}}}$

$\sf{\longrightarrow} \:24 = \dfrac{x}{18}$

$\sf{\longrightarrow} \:x = 18 \times 24$

$\sf{\longrightarrow} \:x = 432$

Sum of the Ages of Boys = 432.

$\rule{300}{1.5}$

Average/Mean age of the class -

• Sum of Observations = 264 + 432
• Number of Observations = 18 + 12

$\sf{\longrightarrow} \: \dfrac{264 + 432}{18 + 12}$

$\sf{\longrightarrow} \: \dfrac{696}{30}$

$\sf{\longrightarrow} \:23.2$

$\therefore$ The Average age of the class is 23.2 years.

Answer 2

Step-by-step explanation:

Find Sum of girls ages

==> 22 = x/12

==> 264

Find the sum of Boys ages .

==> 24 = x/18

==> x = 432

Find the Average of All the students age

==> 696/30

==> 23.2

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