If 12 men and 16 boys can do a piece of work | vedclass

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Question

(A) Let $x$ be the work done by a man in one day and $y$ be the work done by a boy in one day.According to the problem:$5(12x + 16y) = 1 \implies 60x

Vedclass · Accepted Answer

$2:1$

Vedclass · Answer

(A) Let $x$ be the work done by a man in one day and $y$ be the work done by a boy in one day.According to the problem:$5(12x + 16y) = 1 \implies 60x + 80y = 1$ ....$(1)$$4(13x + 24y) = 1 \implies 52x + 96y = 1$ ....$(2)$To solve for $x$ and $y$,multiply equation $(1)$ by $6$ and equation $(2)$ by $5$:$360x + 480y = 6$ ....$(3)$$260x + 480y = 5$ ....$(4)$Subtracting $(4)$ from $(3)$:$100x = 1 \implies x = \frac{1}{100}$Substitute $x = \frac{1}{100}$ into equation $(1)$:$60(\frac{1}{100}) + 80y = 1$$0.6 + 80y = 1$$80y = 0.4$$y = \frac{0.4}{80} = \frac{4}{800} = \frac{1}{200}$The ratio of work done by a man to that of a boy is $x:y = \frac{1}{100} : \frac{1}{200} = 2:1$.

If $12$ men and $16$ boys can do a piece of work in $5 \, \text{days}$,and $13$ men and $24$ boys can do it in $4 \, \text{days}$,then the ratio of the daily work done by a man to that of a boy is:

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