Question

the average age of 120 boys in a class is 17 the average age of group of 30 boys in the class is 21 and the average of another 25 boys in the class is 19 what is the average age of the remaining boys in the class​

Answer 1

Answer

The answer of this question is 1034

Explain

120=17=2040

30=21=631

25=19=475

2040-631+475

2040-1106

1034answer

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

The average age of 120 boys in a class is 17.

The average age of group of 30 boys in the class is 21

and

The average of another 25 boys in the class is 19.

Since,

☆ Total number of boys = 120

☆ Group 1 consists of 30 boys

☆ Group 2 consists of 25 boys

So,

☆ Remaining boys = 120 - 25 - 30 = 120 - 55 = 65

That means,

● Group 3 consists of 65 boys.

● Let average age of 65 boys be x.

Further given that,

Average age of 120 boys = 17

Average age of students of Group 1 = 21

Average age of students of Group 2 = 19

So, Let we represent

☆ Average age of 120 boys is 17 as

$\rm :\longmapsto\:x_{123} \: = \: 17 \: \: and \: \: \: N = 120$

☆ Average age of group 1 of 30 students is 21 as

$\rm :\longmapsto\:x_{1} \: = \: 21 \: \: and \: \: \: N_1 = 30$

☆ Average age of group 2 of 25 students is 19 as

$\rm :\longmapsto\:x_{2} \: = \: 19 \: \: and \: \: \: N_2 = 25$

Average age of group 3 of 55 students is x years as

$\rm :\longmapsto\:x_{ 3} \: = \: x \: \: and \: \: \: N_3 = 65$

We know,

Combined mean is given by

$\red{\rm :\longmapsto\:x_{123} = \dfrac{N_1x_1 + N_2x_2 + N_3x_3}{N}}$

$\rm :\longmapsto\:17 = \dfrac{21 \times 30 + 19 \times 25 + x \times 65}{120}$

$\rm :\longmapsto\:17 = \dfrac{630 + 475 + 65x}{120}$

$\rm :\longmapsto\:2040 = 1105 + 65x$

$\rm :\longmapsto\:2040 - 1105 = 65x$

$\rm :\longmapsto\:935 = 65x$

$\bf\implies \:x = 14.38$