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Question

The mean marks (out of $$100$$) of boys and girls in an examination are $$70$$ and $$73$$, respectively. If the mean marks of all the students in that examination is $$71$$, find the ratio of the number of boys to the number of girls.


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

The correct option is A $$2:1$$
Let the total number of boys be $$x$$ and the total number of girls br $$y$$.
Let the sum of the marks of boys be $$a$$ and the sum of the marks of girls be $$b$$.
Mean marks of boys are $$=70$$
Mean marks of girls are $$=73$$
Therefore,
$$\Rightarrow \dfrac{a}{x}=70$$
$$\Rightarrow a=70x$$
and
$$\Rightarrow \dfrac{b}{y}=73$$
$$\Rightarrow b=73y$$
Now, mean marks of all the students is $$71$$
Therfore,
$$\Rightarrow \dfrac{sum\ of\ the\ marks\ of\ all\ the\ students}{x+y}=71$$
$$\Rightarrow sum\ of\ the\ marks\ of\ all\ the\ students=a+b$$
$$\Rightarrow a+b=70x+73y$$
Therefore,
$$\Rightarrow \dfrac{70x+73y}{x+y}=71$$
$$\Rightarrow 70x+73y=71x+71y$$
$$\Rightarrow2y=x$$
$$\Rightarrow \dfrac{x}{y}=\dfrac{2}{1}$$
$$Hence\ the\ ratio\ is\ 2:1$$

Mathematics

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