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Question 11
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.

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Solution

Let n1 and n2 be the number of boys and girls, respectively.
Given, mean marks (out of 100) of boys (¯x1)=70
And mean marks ( out of 100) of girls (¯x2)=73
Also, given that, mean marks of all the students in the examination (¯x12)=71 [given]
70n1+73n2n1+n2=71
70n1+73n2=71n1+71n2
73n271n2=71n170n1
2n2=n1
n1n2=21 or n1:n2=2:1

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