Question

$5$ women and $2$ men together can finish an embroidary work in $4$ days while $6$ women and $3$ men can finish it in $3$ days. Find the time taken by $1$ women alone to finish the work. Also find the time taken by $1$ man alone to finish the work.

Answer 1

Assume that Women completes the work $W$ in $x$ days

hence, the work done in 1 day $=\frac{W}{x}$

and Men completes the work $W$ in $y$ days

similarly, the work done in 1 day $=\frac{W}{y}$

Now, According to Question Work done in 1 day is $(5\frac{W}{x}+2\frac{W}{y})=\frac{W}{4}$

$\frac{5}{x}+\frac{2}{y}=\frac{1}{4}...\left(1\right)$

Similarly, $\frac{6}{x}+\frac{3}{y}=\frac{1}{3}.....\left(2\right)$

Now, Applying $3eqn\left(1\right)-2eqn\left(1\right)$ we get

$\frac{3}{x}=\frac{3}{4}-\frac{2}{3}\Rightarrow \frac{3}{x}=\frac{1}{12}\Rightarrow x=36days$

Putting this in $eqn\left(2\right)$ we get $y=18days$