Question

2 men and 7 women can together finish a work in 4 days, while 4 men and 4 women can finish it in 3 days. Find the time taken by one man alone to finish the work, and also that taken by one woman alone.

Answer 1

Answer:

${\red{\huge{\underline{\mathbb{solution:-}}}}} \\ \\ let \: one \: women \: can \: finish \: the \: work \: \\ in \: y \: days \: and \: one \: men \: can \: finish \: it \: \\ in \: x \: days. \\ a \: woman \: one \: day \: work \: = \: \frac{1}{y} \\ and \: a \: man \: one \: day \: work \: = \: \frac{1}{x} \\ A.T.Q \\ \frac{2}{x} + \frac{7}{y} = \frac{1}{4} \: and \: \\ \frac{4}{x} + \frac{4}{y} = \frac{1}{3} \\ \\ let \: \frac{1}{x} = p \: and \: \frac{1}{y} = q \\ now \: \: 2p + 7q = \frac{1}{4} - (1) \\ and \: 4p + 4q = \frac{1}{3} - (2) \\ multiplying \:( 1) \: by \: 2\: and \\ subtracting \: . \\ 4p + 14q - 4p - 4q = \frac{1}{2} - \frac{1}{3} \\ 10q = \frac{1}{6} \\ \\ q = \frac{1}{60} \\ putting \: q = \frac{1}{60} \: in \: (1) \\ 2p + 7 (\frac{1}{60} ) = \frac{1}{4} \\ 120p + 7 = \frac{120}{4} \\ 120p + 7 = 30 \\ 120p = 13 \\ p = \frac{13}{120} \\ p = \frac{13}{120} \\ now \: \: p = \frac{1}{x} = 120/13 \\ x = 9.23 \\ and \: \: q = \frac{1}{y} = \frac{1}{60} \\ y = 60 \\ \\ so \: \: one \: woman \: can \: finish \: the \: work \\ in \: 60 \: days \: and \: one \: man \: can \: finish \: the \\ work \: in \: 9.23 \: days.$

hope its help

Answer 2

Answer:

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