Question

$2$ women and $5$ men can together finish an embroidery work in $4$ days, while $3$ women and $6$ men can finish it in $3$ days. Find the time taken by $1$ woman alone to finish the work, and also that taken by $1$ man alone.

Answer 1

Let one woman takes $x$ days to finish the work, and one man takes $y$ days.

A.T.Q:-

$\frac{2}{x}+\frac{5}{y}=\frac{1}{4}$ and $\frac{3}{x}+\frac{6}{y}=\frac{1}{3}$

$\therefore 4(2y+5x)=xy$ $3(3y+6x)=xy$

$\therefore 8y+20x=xy$ …..(i) $\therefore 9y+18x=xy$ ……..(ii)

Multiplying equation (i) by $9$ and equation (ii) by $8$

$72y+120x=9xy$ Put $y=36$ in equation (ii)

$72y+144x=8xy$ $8\times 36+20x=x\times 36$

_______________

$36x=xy$ $\therefore 20x=36x-228$

$\therefore y=36$ $-16x=-288$

$\therefore x=18$.