Question

8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boys can finish it in 14

days. Find the time taken by the one girl alone that by one boy alone to finish the work​

Answer 1

Answer:

$Let \: one \: girl \: alone \\ can \: finish \:the \\work \:in \: x \:days \: and \\one \: boy \: alone \: can \: finish \\the \: work \: in \: y \: days$

$Part \: of \:the \: work \: done \: by \: the \\girl \: in \: one \:day = \frac{1}{x}$

$Part \: of \:the \: work \: done \: by \: the \\boy \: in \: one \:day = \frac{1}{y}$

$Given , \: 8 \: girls \: and \: 12 \:boys \: can \\finish \: the \: work \: in \: 10 \:days$

$i.e ., \frac{8}{x} + \frac{12}{y} = \frac{1}{10}$

$\implies 10\left( \frac{8}{x} + \frac{12}{y}\right) = 1$

$\implies \frac{80}{x} + \frac{120}{y} = 1 \:--(1)$

$Given , \: 6 \: girls \: and \: 8 \:boys \: can \\finish \: the \: work \: in \: 14 \:days$

$i.e ., \frac{6}{x} + \frac{8}{y} = \frac{1}{14}$

$\implies 14\left( \frac{6}{x} + \frac{8}{y}\right) = 1$

$\implies \frac{84}{x} + \frac{112}{y} = 1 \:--(2)$

$Let \: \frac{1}{x} = a , \: \frac{1}{y} = b \: in \\equation \: (1) \:and \: (2) , then$

$80a + 120b = 1 \: ---(3)$

$84a + 112b = 1 \: ---(4)$

/* By solving (3) and (4) we get,

$a = \frac{1}{140} = \frac{1}{x} \\\implies x = 140$

$and \: b = \frac{1}{280}= \frac{1}{y}$

$\implies y = 280$

Therefore.,

$One \: girl \: alone \: can \: finish \: the \: work \\ in \: 140 \:days \: and$

$One \: boy \: alone \: can \: finish \: the \: work \\ in \: 280 \:days$

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