3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and child does half the work a man does. How many women alone can complete this work in 7 days?

The correct option is A

7

Let 1 woman`s 1 day`s work = x

Then, 1 man`s 1 day`s work =$\frac{x}{2}$ and 1 child`s 1 day`work = $\frac{x}{4}$

So, $\frac{3x}{2}+4x+\frac{6x}{4}=\frac{1}{7}$

$\frac{28x}{4}=\frac{1}{7}$

x = $\frac{1}{49}$

1 woman alone can complete the work in 49 days

So, to complete the work in 7 days, number of women required = $\frac{49}{7}$ = 7