The mean marks (out of 100) of boys and girls | vedclass

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(D) Let the number of boys be $n_1$ and the number of girls be $n_2$.Using the formula for the combined mean:$\bar{x} = \frac{n_1 \bar{x}_1 + n_2 \bar

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$2 : 1$

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(D) Let the number of boys be $n_1$ and the number of girls be $n_2$.Using the formula for the combined mean:$\bar{x} = \frac{n_1 \bar{x}_1 + n_2 \bar{x}_2}{n_1 + n_2}$Given that $\bar{x}_1 = 70$,$\bar{x}_2 = 73$,and the combined mean $\bar{x} = 71$:$71 = \frac{n_1 	imes 70 + n_2 	imes 73}{n_1 + n_2}$Multiplying both sides by $(n_1 + n_2)$:$71(n_1 + n_2) = 70n_1 + 73n_2$$71n_1 + 71n_2 = 70n_1 + 73n_2$Rearranging the terms to solve for the ratio:$71n_1 - 70n_1 = 73n_2 - 71n_2$$n_1 = 2n_2$Therefore,the ratio of the number of boys to the number of girls is:$\frac{n_1}{n_2} = \frac{2}{1}$Thus,the required ratio is $2 : 1$.

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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