Question

The mean marks of boys and girls in an examination are 70 and 73 respectively . If the mean mark of the entire student in that examination is 71 , find the ratio of the number of boys to the number of girls

Answer 1

Hi there!

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What is Mean?

The average of a given set of numbers is called the Arithmetic mean, or simply the mean, of the given numbers.

Mean = $\frac{Sum \: of \: observations }{Number \: of \: observations }$

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For your solution to the given question refer to the attachment.

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Answer 2

$\underline{\bold{Solution:-}}$

Let, the number of boys be x and number of girls be y.

$\\Mean \: marks \: of \: boys \\ = \frac{Total \: marks \: of \: boys }{Total \: number \: of \: boys} \\ \\ 70 = \frac{Total \: marks \: of \: boys}{ x } \\ \\ Total \: marks \: of \: boys = 70x \: \: ......(1) \\ \\\\ Mean \: marks \: of \: boys \\ = \frac{Total \: marks \: of \: girls }{Total \: number \: of \: girls} \\ \\ 73 = \frac{Total \: marks \: of \: girls}{y} \\ \\ Total \: marks \: of \: girls = 73y \: \: .....(2) \\\\ \\ Mean \: marks \: of \: entire \: students \\ = \frac{Total \: marks \: of \:students}{Total \: number \: of \: students } \\ \\ Mean \: marks \: of \: entire \: students \\ = \frac{Marks \: of \:boys + Marks \: of \: girls}{ Number \: of \: boys + Number \: of \: girls } \\ \\ from \: eq \: (1) \: and \: (2) \\ \\ 71 = \frac{70x + 73y}{x + y} \\ \\ 71(x + y) = 70x + 73y \\ \\ 71x + 71y = 70x + 73y \\ \\ 71x - 70x = 73y - 71y \\ \\ x = 2y \\ \\ \frac{x}{y} = \frac{2}{1} \\ \\ \frac{Number \: of \: boys}{Number \: of \: girls} = \frac{2}{1}$
So, number of boys : number of girls = 2:1