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. [4 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Let the work completed by 1 man in a day be $m$

& that by a woman be $w$

Then, 1 man's 1 day's work $=\frac{1}{m}$

Then, 1 woman's 1 day's work $=\frac{1}{w}$

2 women and 5 men can together finish an embroidery work in 4 days

$\Rightarrow \frac{2}{w}+\frac{5}{m}=\frac{1}{4}$

$\Rightarrow 2x+5y=\frac{1}{4}\dots \dots \left(i\right)$ where $\frac{1}{w}=x,\frac{1}{m}=y$

Similarly,

$\frac{3}{w}+\frac{6}{m}=\frac{1}{3}$

$\Rightarrow 3x+6y=\frac{1}{3}\dots \dots \left(ii\right)$ where $\frac{1}{w}=x,\frac{1}{m}=y$

Solving (i) and (ii) we get,

$2x=\frac{1}{4}-5y$

$x=\frac{1-20y}{8}$

Substituting value of x in (ii)

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

$\Rightarrow 3\left(\frac{1-20y}{8}\right)+6y=\frac{1}{3}$

$\Rightarrow \frac{3-60y+48y}{8}=\frac{1}{3}$

$\Rightarrow y=\frac{1}{36}$

Now, $x=\frac{1-20y}{8}$

$x=\frac{1-20\left(\frac{1}{36}\right)}{8}$

$\Rightarrow x=\frac{1}{18}$

$\therefore y=\frac{1}{36}$

$\Rightarrow \frac{1}{m}=\frac{1}{36}\Rightarrow m=36$

$\therefore$ one man alone can complete the wok in 36 days

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

$\Rightarrow \frac{1}{w}=\frac{1}{18}\Rightarrow w=18$

$\therefore$ one woman alone can complete the wok in 18 days