Question

the average weight of all male stars in a multi star Bollywood movie is 71.2 kg. where as average weight of all female co stars is 59.8kg. if the mean weight of male and female stars acting in the movie is 60kg. find the ratio of number of male stars to the number of female co stars acting in the movie.​

Answer 1

$Let \: Number \: of \: male \: stars \: in \: a \\ multi \:star \: Bollywood = x$

$Average\: weight \:of \:male \:stars = 71.2 \:kg$

$Sum \: of \: weights \:of \: male \:stars = 71.2x$

$Let \: Number \: of \: Female \: stars \: in \: a \\ multi \:star \: Bollywood = y$

$Average\: weight \:of \:female \:stars = 59.8\:kg$

$Sum \: of \: weights \:of \: male \:stars = 59.8y$

$Mean \: weight \:of \:male \: and \: female \\stars \: acting \:in \:the \:movie = 60 \:kg$

$\implies \frac{71.2x + 59.8y}{x+y} = 60$

$\implies 71.2x + 59.8y = 60(x+y)$

$\implies 71.2x + 59.8y = 60x+60y$

$\implies 71.2x - 60x = 60y - 59.8y$

$\implies 11.2x = 0.2y$

$\implies \frac{x}{y} = \frac{0.2}{11.2}$

$\implies \frac{x}{y} = \frac{2}{112}$

$\implies \frac{x}{y} = \frac{1}{56}$

$\implies \frac{Number \: male \: stars }{Number \:of \:Female \:stars } = \frac{1}{56}$

Therefore.,

$\red {The\: ratio\: of\: number\: of \:male}\\\red{ stars\: to\: the \:number \:of \:female}\\\red{ co \:stars\: acting \:in \:the\: movie.}\green {= \frac{1}{56} }$

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