If 4 men and 2 women can complete a task in 6 days and 2 men and 4 women can complete a task in 10 days then how many women are required to complete a task in a day?

Let 1 man's 1 day work = m, 1 woman's 1 day work = w. From first condition: 4m + 2w = 1/6. From second: 2m + 4w = 1/10. Solving: multiply first by 2: 8m + 4w = 1/3. Subtract second from this: 6m = 1/3 - 1/10 = 7/30, so m = 7/180. Then w = 13/720. For 1 day, let x women be needed: x × w = 1, so x = 1/w = 720/13 ≈ 55.4, which rounds to 54 women.