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.

# 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.

1. A

100 and 50

2. B

50 and 100

3. C

150 and 100

4. D

100 and 150

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### Solution:

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

${n}_{1}+{n}_{2}=150$                            …(i)

We have,

$\overline{{X}_{1}}=$Mean weight of boys $=70\mathrm{kg}$

$\overline{{X}_{2}}=$ Mean weight of girls

$\overline{X}=$ Mean weight of all student

$\begin{array}{l}\therefore \overline{X}=\frac{{n}_{1}\overline{{X}_{1}}+{n}_{2}\overline{{X}_{2}}}{{n}_{1}+{n}_{2}}\\ ⇒ 60=\frac{{n}_{1}×70+{n}_{2}×55}{{n}_{1}+{n}_{2}}\\ ⇒ 60\left({n}_{1}+{n}_{2}\right)=70{n}_{1}+55{n}_{2}\\ ⇒ 60{n}_{1}+60{n}_{2}=70{n}_{1}+55{n}_{2}\end{array}$

…(ii)

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

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

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