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. Finish the time taken by 1 woman alone to finish the work , and also that taken by 1 man alone.

Answer 1

Number of days required

For women be x

For men be y

Work done by women in 1 day= $\frac{1}{x}$

Work done by men in 1 day = $\frac{1}{y}$

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

$3(\frac{3}{x}+\frac{6}{y})=1$

Let $\frac{1}{x}=pand\frac{1}{y}=q$.

$\therefore 8p+20q=1,9p+18q=1$

From both the equation

$9\frac{(1-20q)}{8}+18q=1$

$q=\frac{1}{36}$

$p=\frac{1}{18}$

$\therefore$ 1 women will finish work in 18 days