Question

4 men or 6 women can finish a work in 16 days. In how many days the same work is completed by 2 by men and 9 women?

Answer 1

1/4+1/6=16. 1/2+1/9=0=?

Answer 2

2 men and 9 women can do the same piece of work in 8 days

Step-by-step explanation:

Given:

Let 1 man can do $(\frac{1}{x})$ of work per day and 1 woman can do $(\frac{1}{y} )$ of work per day .

We know that 4 men or 6 women can finish a work in 16 days,

$4\times (\frac{1}{x} )\times 16 = 1$  

⇒ x=64  

$6\times (\frac{1}{y} ) \times 16 =1$  

⇒ y = 96

Now, the work completed by 2 by men and 9 women,

$[ (2\times (\frac{1}{64} ))+(9\times(\frac{1}{96} ))]\times z = 1$

⇒ $[ \frac{1}{32} +\frac{3}{32}]\times z = 1$

⇒  $[\frac{1+3}{32}]\times z = 1$

⇒ $[\frac{4}{32}]\times z = 1$

⇒ $[\frac{1}{8}]\times z = 1$

⇒ z = 8

Therefore 2 men and 9 women can do the same piece of work in 8 days