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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,
ax=70
a=70x
and
by=73
b=73y
Now, mean marks of all the students is 71
Therfore,
sum of the marks of all the studentsx+y=71
sum of the marks of all the students=a+b
a+b=70x+73y
Therefore,
70x+73yx+y=71
70x+73y=71x+71y
2y=x
xy=21
Hence the ratio is 2:1

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