The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys in the class is 70 kg and that of girls is 55 kg. The number of boys and the number of girls in the class, are respectively.

A
100 and 50
B
50 and 100
C
150 and 100
D
100 and 150

Solution:

Let the number of boys and girls in the class be $n_{1}$ and $n_{2}$ respectively. Then,

$n_{1} + n_{2} = 150$ …(i)

We have,

$\bar{X_{1}} =$ Mean weight of boys $= 70 kg$ $\Rightarrow 10 n_{1} = 5 n_{2} \Rightarrow 2 n_{1} = n_{2}$

$\bar{X_{2}} =$ Mean weight of girls $= 55 k g$

$\bar{X} =$ Mean weight of all student $= 60 k g .$

$\begin{array}{l} ∴ \bar{X} = \frac{n_{1} \bar{X_{1}} + n_{2} \bar{X_{2}}}{n_{1} + n_{2}} \\ \Rightarrow 60 = \frac{n_{1} \times 70 + n_{2} \times 55}{n_{1} + n_{2}} \\ \Rightarrow 60 (n_{1} + n_{2}) = 70 n_{1} + 55 n_{2} \\ \Rightarrow 60 n_{1} + 60 n_{2} = 70 n_{1} + 55 n_{2} \end{array}$

$\Rightarrow 10 n_{1} = 5 n_{2} \Rightarrow 2 n_{1} = n_{2}$ …(ii)

From (i) and (ii), we have $n_{1}$ = 100, $n_{2}$ = 50

Hence, there are 50 boys and 100 girls in the class.

Solution:

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