One man,3 women,and 4 boys can do a work in 9 | vedclass

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(B) Let $M, W, B$ be the work done by $1$ man,$1$ woman,and $1$ boy in $1$ hour respectively.From the given data:$1M + 3W + 4B = \frac{1}{96}$ ...$(i)

Vedclass · Accepted Answer

$43 \frac{7}{11}$

Vedclass · Answer

(B) Let $M, W, B$ be the work done by $1$ man,$1$ woman,and $1$ boy in $1$ hour respectively.From the given data:$1M + 3W + 4B = \frac{1}{96}$ ...$(i)$$2M + 8B = \frac{1}{80} \implies 1M + 4B = \frac{1}{160}$ ...$(ii)$$2M + 3W = \frac{1}{120}$ ...$(iii)$Subtracting $(ii)$ from $(i)$:$(1M + 3W + 4B) - (1M + 4B) = \frac{1}{96} - \frac{1}{160}$$3W = \frac{5-3}{480} = \frac{2}{480} = \frac{1}{240}$So,$3$ women can do the work in $240$ hours.From $(iii)$,$2M = \frac{1}{120} - 3W = \frac{1}{120} - \frac{1}{240} = \frac{2-1}{240} = \frac{1}{240}$.So,$2$ men can do the work in $240$ hours,which means $1$ man can do it in $480$ hours.From $(ii)$,$4B = \frac{1}{160} - 1M = \frac{1}{160} - \frac{1}{480} = \frac{3-1}{480} = \frac{2}{480} = \frac{1}{240}$.So,$4$ boys can do the work in $240$ hours,which means $1$ boy can do it in $960$ hours.Now,for $5$ men and $12$ boys:Work per hour $= 5 	imes (\frac{1}{480}) + 12 	imes (\frac{1}{960}) = \frac{5}{480} + \frac{12}{960} = \frac{10}{960} + \frac{12}{960} = \frac{22}{960} = \frac{11}{480}$.Time taken $= \frac{480}{11} = 43 \frac{7}{11}$ hours.

One man,$3$ women,and $4$ boys can do a work in $96$ hours,$2$ men and $8$ boys can do it in $80$ hours,and $2$ men and $3$ women can do it in $120$ hours. In how many hours can it be done by $5$ men and $12$ boys? (in hours)

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