3 men, 4 women and 6 boys together can complete a work in 6 days. A woman does triple the work a man does and a boy does half the work a man does. How many women alone will be able to complete this work in 4 days?

As per the question,

Let the man completed $$x$$ work, women completed $$3x$$ work and children completed $$ \dfrac{x}{2}$$ work.

Hence, the ratio of man, women and children's work ratio $$=x:3x:\dfrac{x}{2}=2:6:1$$

Let one man's one day's work =a, one women's one day's work =b and one children's one day's work =c

Now, as per the condition,4 women is working for 6 days so total work will be finish $$=4b\times 6 =24b$$

Hence, total contribution of work by women $$ 24b=\dfrac{6}{9}=\dfrac{2}{3}$$

$$ b=\dfrac{1}{36}$$

So, one women can finish the work in 36 days,

Let n number of women completing the work in 4 days,

So, $$\dfrac{36}{n}=4$$

$$\dfrac{36}{4}=n$$

$$n=9$$

Hence 9 women can finish the work in 4 days.