3 men and 4 boys can complete a certain work | vedclass

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(D) Let the work done by $1$ man in $1$ day be $M$ and by $1$ boy in $1$ day be $B$.According to the problem:$8(3M + 4B) = 1$ (Total work)$24M + 32B =

Vedclass · Accepted Answer

$12$

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(D) Let the work done by $1$ man in $1$ day be $M$ and by $1$ boy in $1$ day be $B$.According to the problem:$8(3M + 4B) = 1$ (Total work)$24M + 32B = 1$ .....$(1)$$6(4M + 4B) = 1$$24M + 24B = 1$ .....$(2)$Subtracting equation $(2)$ from $(1)$:$(24M + 32B) - (24M + 24B) = 1 - 1$$8B = 0$,which implies $B = 0$ (The boys contribute no work).Substituting $B = 0$ in equation $(2)$:$24M = 1 \Rightarrow M = 1/24$.So,$1$ man completes the work in $24$ days.We need to find the time taken by $2$ men and $4$ boys:Work done by $(2M + 4B)$ in $1$ day $= 2(1/24) + 4(0) = 2/24 = 1/12$.Therefore,$2$ men and $4$ boys will finish the work in $12$ days.

$3$ men and $4$ boys can complete a certain work in $8$ days,while $4$ men and $4$ boys can complete the same work in $6$ days. Then $2$ men and $4$ boys will finish it in ........ days.

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