Question

the mean weight of 150 students in a certain class is 30 kg . the mean weight of boys in the class is 40 kg and that of the girls is 25 kg . find the number of boys and girls in the class​

Answer 1

Answer:

The number of boys is 100 and the number of girls is 50.

Step-by-step explanation:

Let the number of boys be $n_{x}$ and the number of girls be $n_{y}$.

Total students = 150.

That is: $n_{x}+n_{y}=150$...(i)

The combined mean formula is:

$Comnined\ mean=\frac{n_{x}\bar x+n_{y}\bar y}{n_{x}+n_{y}}$

The mean weight of whole class is 30 kg.

The mean weight of boys is, 40 kg and that of girls is 25 Kg.

$Comnined\ mean=\frac{n_{x}\bar x+n_{y}\bar y}{n_{x}+n_{y}}\\30=\frac{n_{x}\times 40+n_{y}\times 25}{150}\\40n_{x}+25n_{y}=4500...(ii)$

Solve (i) and (ii) simultaneously as follows:

$n_{x}+n_{y}=150\ ]\times25\\40n_{x}+25n_{y}=4500$

$25n_{x}+25n_{y}=3750\\-40n_{x}-25n_{y}=-4500$

$15n_{y}=750\\n_{y}=50$

Then the number of boys is:

$n_{x}=150-n_{y}=150-50=100$

Thus, the number of boys is 100 and the number of girls is 50.

Answer 2

AnswEr :

Let the Boys in the Class be n, and Girls in the Class be (150 – n).

$\bigstar\:\boxed{\sf Mean =\dfrac{Sum \:of \:Terms}{Number \:of \:Terms}}$

$\rule{120}{1}$

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$:\implies\textsf{Total Weight of Class = (Boys + Girls) Weight}\\\\\\:\implies\sf Mean \times Number = (Mean \times Boys \: No.) + (Mean \times Girls \: No.)\\\\\\:\implies\sf(30 \times 150) = (40 \times n) + (25 \times (150 - n))\\\\\\:\implies\sf4500 = 40n + 3750 - 25n\\\\\\:\implies\sf4500 - 3750 = 40n - 25n\\\\\\:\implies\sf750 = 15n\\\\\\:\implies\sf \cancel\dfrac{750}{15} = n\\\\\\:\implies\sf n = 50$

$\rule{200}{2}$

• S P E C I F I C ⠀N U M B E R S :

↠ Boys = n = 50

↠ Girls = (150 – n) = (150 – 50) = 100

⠀

∴ There are 50 boys and 100 girls in class.