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
B
2:1
C
1:2
D
2:3

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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