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Question

The average score of boys in an examination of a school is $$71$$ and that of girls is $$73$$. The average score of the school in that examination is $$71.8$$. The ration of the number of boys to the number of girls appeared in the examination, is


A
3:2
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B
3:4
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C
1:2
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D
2:1
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Solution

The correct option is A $$3:2$$
Let there be $$n_1$$ boys and $$n_2$$ girls.
and  $$\overline{X_1}$$ and $$\overline{X_2}$$ be the average scores of boys and girls respectively.
Then $$\bar { { X }_{ 1 } } =71,\bar { { X }_{ 2 } } =63$$ and $$\overline{X} = 71.8$$
$$\therefore \quad     \overline{X} = \displaystyle\frac{n_1\overline{X_1} + n_2\overline{X_2}}{n_1+n_2}$$
$$\Rightarrow \quad   71.8 = \displaystyle\frac{n_1\times71 + n_2\times73}{n_1+n_2}$$
$$\Rightarrow \quad 71.8n_1 +  71.8n_2 = 71n_1 + 73n_2$$
$$\Rightarrow \quad 0.8n_1 = 1.2n_2 \quad \Rightarrow 8n_1 = 12n_2$$
$$\Rightarrow \quad \displaystyle\frac{n_1}{n_2} = \displaystyle\frac{12}{8} = \displaystyle\frac{3}{2}$$

Mathematics

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