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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.
Solution
Let x and y be the number of boys and girls, respectively.
Given, mean marks (out of 100) of boys `(barx_1) = 70`
And mean marks (out of 100) of girls `(barx_2) = 73`
Also, given that, mean marks of all the students in the examination `(barx_12) = 71`
Now, using the formula,
Combined mean, `(barx_12) = (barx_1n_1 + barx_2n_2)/(n_1 + n_2) = 71` ...[Given]
∴ `(70n_1 + 73n_2)/(n_1 + n_2) = 71`
⇒ 70n1 + 73n2 = 71n1 + 71n2
⇒ 73n2 – 71n2 = 71n1 – 70n1
⇒ 2n2 = n1
⇒ `n_1/n_2 = 2/1` or n1 : n2 = 2 : 1
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