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

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

Solution:
Let 1 woman's 1 day work = x.
Then, 1 man's 1 day work = x/2 and 1 child's 1 day work x/4.

ATQ,
(3x/2) + 4x + (6x/4) = 1/7
⇒ 28x/4 = 1/7
∴ x = 1/49

1 woman alone can complete the work in 49 days.
So, to complete the work in 7 days, number of women required = 49/7 = 7.