Question

9 children do a work in 360 days 18 men do same work in 72 days and 12 women do same work 162 days.in how many days 4 men 12 women and 10 children do that work.?

Answer 1

$9 \: children \: do \: in \: 360 \: days \\ 1 \: child \: does \: in \: 360 \times 9 \: days \\ in \: one \: day \: work \: done \: by \: child \: \\ \: \: \: \: \: \: \: \: = \frac{1}{3240} \\ similiarly \\ \: in \: one \: day \: work \: by \: man \: \\ \: \: \: \: \: \: \: \: \: = \frac{1}{18 \times 72} \\ in \: one \: day \: work \: by \: woman \\ \: \: \: \: \: \: \: \: = \frac{1}{12 \times 162} \\ 10 \: \: children \: in \: one \: day \: work \: \\ \: \: \: \: \: \: = \frac{10}{3240} = \frac{1}{324} \\ 12 \: women \: work \: in \: a \: day \\ \: \: \: \: \: = \frac{12}{1944} = \frac{1}{162} \\ 4men \: work \: in \: one \: day \\ \: \: \: \: \: \: = \frac{4}{18 \times 72} = \frac{1}{324} \\ work \: in \: a \: day \: by \: 4 \: men \: 12 \: women \: and \: 10 \: children \\ \: \: \: \: \: \: \: \: = \frac{1}{324} + \frac{1}{162} + \frac{1}{324 } \\ \: \: \: \: \: \: = \frac{1 + 2 + 1}{324} = \frac{4}{324} = \frac{1}{81} \\ so \: ans \: is \: 81 \: days$
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