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the mean marks for a french test in a class of 30 boys and 20 girls are 60 and 70 respectively. find the mean mark for the whole class.
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the mean marks for a french test in a class of 30 boys and 20 girls are 60 and 70 respectively. find the mean mark for the whole class.
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Mathematics
3 years
2021-07-23T13:14:10+00:00
2021-07-23T13:14:10+00:00 1 Answers
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Answers ( )
Step-by-step explanation:
Let, the number of boys be x and number of girls be y.
\begin{gathered}\\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} \\ \\\end{gathered}
Meanmarksofboys
=
Totalnumberofboys
Totalmarksofboys
70=
x
Totalmarksofboys
Totalmarksofboys=70x……(1)
Meanmarksofboys
=
Totalnumberofgirls
Totalmarksofgirls
73=
y
Totalmarksofgirls
Totalmarksofgirls=73y…..(2)
Meanmarksofentirestudents
=
Totalnumberofstudents
Totalmarksofstudents
Meanmarksofentirestudents
=
Numberofboys+Numberofgirls
Marksofboys+Marksofgirls
fromeq(1)and(2)
71=
x+y
70x+73y
71(x+y)=70x+73y
71x+71y=70x+73y
71x−70x=73y−71y
x=2y
y
x
=
1
2
Numberofgirls
Numberofboys
=
1
2