Question

$4$ men and $4$ boys can do a piece of work in $3$ days. While $2$ men and $5$ boys can finish in $4$ days. How would it take for $1$ boy to do it? How long would it take to $1$ men do it?

Answer 1

Let a boy do $x^{th}$ function of work in one day and a man $y^{th}$ function

$\Rightarrow 3(\frac{4}{x}+\frac{4}{y})=1$ and $4(\frac{5}{x}+\frac{2}{y})=1$

$\Rightarrow \frac{4}{x}+\frac{4}{y}=\frac{1}{3}...\left(1\right)$ and $\frac{10}{x}+\frac{4}{y}=\frac{1}{2}$ ...(2)

equation (1) - equation (2) $\frac{4-10}{x}=\frac{1}{3}-\frac{1}{2}\Rightarrow \frac{6}{x}=\frac{1}{6}\Rightarrow x=36$

In equation (1) $\frac{4}{36}+\frac{4}{y}=\frac{1}{3}$ $\Rightarrow \frac{4}{y}=\frac{3}{9}-\frac{1}{9}$ $\Rightarrow y=\frac{36}{2}=18$

$\Rightarrow$ A Boy will do the work in 36 days and in 18 days