Question

55. Average age of 36 children of the class is
15 yr. 12 more children joined whose
average age is 16 yr. What is the average
age of all the 48 children together?
(1) 15.25 yr
(2) 155 yr
(3) 15.3 yr
(4) 15.4 yr​

Answer 1

Answer:

Option (1) 15.25

The average age of 48 children together is 15.25 years.

Step-by-step explanation:

Number of children = 36

Average age of children = 15 years

New children = 12 ; Their average age = 16

Total children = 48

Total Average = ??

Formula used :

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

___________________

Case I -

• Number of observations = 36
• Average = 15
• Sum of observations = y

$\sf{\longrightarrow{15 = \dfrac{y}{36}}}$

$\sf{\longrightarrow{y = 15 \times 36}}$

$\sf{\longrightarrow{y = 540}}$

Sum of Observations = 540

___________________

Case II -

12 new students join, and their average age is 16.

• Number of observations = 12
• Average = 16
• Sum of observations = x

$\sf{\longrightarrow{16 = \dfrac{x}{12}}}$

$\sf{\longrightarrow{x = 16 \times 12}}$

$\sf{\longrightarrow{x = 192}}$

Sum of observations = 192

___________________

★ Average age of all children :

• Number of observations = 48
• Sum of observations = (540 + 192) = 732

$\sf{\longrightarrow{ \dfrac{732}{48}}}$

$\sf{\longrightarrow{15.25}}$

Average age of all children = 15.25 years.

Therefore, the average age of 48 children together is 15.25 years.

Answer 2

Answer:

Given :-

• Average age of 36 children of the class is 15 years.
• 12 more children joined whose average age is 16 years.

To Find :-

• What is the average age of all 48 children together.

Formula Used :-

$\clubsuit$ Average Formula :

$\longmapsto \sf\boxed{\bold{\pink{Average =\: \dfrac{Sum\: Of\: Observations}{Total\: Number\: Of\: Observations}}}}$

Solution :-

${\small{\bold{\purple{\underline{In\: the\: {1}^{st}\: Case\: :-}}}}}$

Given :

$\mapsto$ Average age of 36 children of the class is 15 years.

Let, the sum of observations is x

• Total number of observations = 36
• Average = 15

According to the question by using the formula we get,

$\implies \sf 15 =\: \dfrac{x}{36}$

By doing cross multiplication we get,

$\implies \sf x =\: 36(15)$

$\implies \sf x =\: 36 \times 15$

$\implies \sf\bold{\green{x =\: 540}}$

$\rule{300}{2}$

${\small{\bold{\purple{\underline{In\: the\: {2}^{nd}\: Case\: :-}}}}}$

$\mapsto$ 12 more children joined whose average age is 16 years.

Let, the sum of observations be x

Given :

• Total number of observations = 12
• Average = 16

According to the question by using the formula we get,

$\implies \sf 16 =\: \dfrac{x}{12}$

By doing cross multiplication we get,

$\implies \sf x =\: 12(16)$

$\implies \sf x =\: 12 \times 16$

$\implies \sf\bold{\green{x =\: 192}}$

$\rule{300}{2}$

Now, we have to find the average age of all 48 children together :

Given :

$\mapsto$ Sum of Observations :

$\leadsto$ $\sf 540 + 192$

$\leadsto$ $\sf\bold{\green{732}}$

$\mapsto$ Number of Observations :

$\leadsto$ $\sf\bold{\green{48}}$

According to the question by using the formula we get,

$\implies \sf Average\: age =\: \dfrac{732}{48}$

$\implies \sf Average\: age =\: \dfrac{\cancel{732}}{\cancel{48}}$

$\implies \sf\bold{\red{Average\: age =\: 15.25\: years}}$

$\therefore$ The average age of all 48 children together is 15.25 years .

Hence, the correct options is option no (1) 15.25 years .